Late night Bearings and Circle theorems

Added: 2026-05-06

[00:00:01]last of the Moheakans of the April late night studies.

[00:00:10]Um, those of you who just popped in, well, we have a crash uh 12-hour crash course coming up on Monday. So, you WhatsApp this number three 3101306.

[00:00:21]It's streaming at the bottom of the YouTube um page. you WhatsApp that number to join that crash course which is 12 hours and I got be. So tonight is not matrix multiplication but I I said I will just you know jump out with that little matrix multiplication real fast so we can see what's happening. Right?

[00:00:43]So we we're going to do bearings and circle theorem uh question nine. But let's just do a quick matrix multiplication review because I I just want to beta test this because I'm posting this on the website tonight. I have a circle theorems thing that I'm still fixing. I have to post that on the website. I have to post back POB. POB had to fix. There was some mix up in the papers. I have to post back that. I there's an issue in some of the maths PDF that's kind of messing up how the answers are displayed in some things. I need to fix that as well. So, I'm hoping to do all of that tonight. I should be in Guyana later this week, too. Maybe on Friday. I'll be in Guyana there. So, um a lot to do. Uh so, let's begin this M multiplication. Quick revision. Let's just jump right into it into this and make sure we know how to multiply matrices. Right? Now, remember a matrix that's this thing in maths where you have like where you have like uh sure uh you put it in brackets and you put you put some numbers in the brackets like that and they're like different spots.

[00:01:51]It's like they're in different different little shells there. Little shells.

[00:01:55]That's matrix matrices. Everybody seeing the mic the volume low on this end? Let me see if I can fix that. Um, is it better now? It should be better now.

[00:02:05]What about on Tik Tok? Tik Tok. Your volume good.

[00:02:09]Mute. Unmute.

[00:02:11]Audio mixer primary. Yeah, it should be good for all. Right. Um, so yeah, that's matrices. And if I click begin, they'll tell me about matrix sizes. A matrix is named by its dimension. Like you call it by its dimension. Let me just move my thing out of the way here. So this matrix here is a 2x one matrix. It has two rows. So two rows, one column. So if you didn't know, now you know. This matrix here has how many? What? How many rows? It's a one row, two column.

[00:02:49]This would be a 2x two. Two rows, two columns. And because it's the same, it's also called a square matrix, right? Um everybody if you understand type, I understand in the chat that is common. Sometime they ask you to name the size of the matrix. This has three rows, three columns also a square matrix. What is this? Two rows, four columns. So, I'm posting this tonight on the website. If you need some if you need to run it through by yourself, you should see it by the morning. So, you all tell me what to write on the bottom here. You all seen this? How many rows? How many columns?

[00:03:22]What should I write on the on the underneath here? Um, definitely one row, two rows. How many columns? One, two, three. So, three columns. As you continue to the next rounds, right?

[00:03:38]So, this is about matrix multiplication.

[00:03:40]Matrix multiplication, you run down the row and then you run down the column. So you run down the row to give me my hint and then you run down the column, right?

[00:03:48]So the five will multiply by what? By the corresponding one and notice you can't mult you can't use the five and one again. That's the rule. That's the rule. So then you use the three multiply by the four.

[00:04:04]Catch it? So you run down the row, run down the column. So 5 by 1 is 5 and 3x 4 is 12 and you don't add those two numbers. That's it. The answer is 512.

[00:04:15]That's it. Mhm. Right out of 10. I'm sure you'll understand that. All right.

[00:04:20]Let's go to the next rounds. We have a we really come here to do bearings. My class voted on doing bearings and circle terms. You could have to use the number twice like this. You see I put two dots on these numbers here. That means they're going to get used twice. So I'm going to multiply this dark blue row by the column here. Then the light blue row get to multiply by the column. So this one is a little different than before.

[00:04:41]So row and you're going down the row. So this multiply with this. Go down the row here. Same thing like this. Now pick the one there. Now that's the top answer there as the top answer. This actually going to boil along together to give you one answer. And then you go 5 by 7 and 6 by 1. Check that you get 1122.

[00:05:09]That making sense? Everybody's clear there, Crystal.

[00:05:14]You understand how we get 11? Well, you need to take out your calculator and work it out. -1 * -7. So that's like -1 * -7 is 7. You should know that. And then 4 by one. So then you're just going to add or go by calculator. See, you see how this calculator beed me.

[00:05:42]Oh gosh, my calculator. Give me my chance now boy.

[00:05:46]Right tree doing me this turn you off and all kind of thing.

[00:05:58]I ain't using that again. That's the final stroke. That's the final stroke.

[00:06:03]actually going to use it again. But he used he used tonight. Forget he. Um so, so yeah, we we we do this one one by check. Boom. We correct, right? Let's go on to the next thing. Um teachers, if you want to use this to teach your class, it's going to be up on my website on curvin Springer. Feel free like yourself. Now what this doing is talking about compatibility of multiplication.

[00:06:33]Why is in the chat if you know what this question is about? Have you seen this question in CXE where they ask you if these matrices can multiply? You know I'm talking about can these matrices multiply. And what they're trying to say here is if you write the size of the matrices the two numbers on the inside is the indication that they could multiply. There's a reason for this but we're not going into that tonight. So the the number of columns in the first matrix must be equal to the number of rows in the second matrix. That's just so that the lineup could happen that you have things to multiply compatible. So is this are these two compatible? That's what they're asking here. Can these two matrices multiply based on their sizes?

[00:07:13]Cuz this is a 2x3 matrix.

[00:07:16]Two rows, three columns, and this is a 3x4 matrix. So can they can they multiply? Yes or no? And that's that's that's your question, Chad.

[00:07:27]Plenty of people saying no. Samantha saying yes. Um Samantha is normally get things correct. So they double check.

[00:07:33]Can they multiply? What they feel? Hey, they look heaven boy. Are you going go on one L Y X O U I 749 and tell me what you see on that profile page.

[00:07:47]Yes guys, this can multiply. Why? Why you all saying it can multiply the number? Wait, let me make sure. The number of columns in the first matrix, how many columns in this matrix? Three. 1 2 3 must be equal to the number of rows in the second matrix. Remember, it's always row by column. Row by column. So, yes, this can multiply. This has three columns.

[00:08:12]So, three columns and um three rows. So, you can multiply. What about this one? Can the second one multiply? Can this one multiply?

[00:08:25]Is the number of columns in the first matrix equal to the number of rows in the second matrix? Yes or no?

[00:08:35]The number of columns must be equal to the number of rows.

[00:08:40]So we can see this is a the first matrix is a 3x2 matrix. The next matrix is also a 3x2 matrix. It can't multiply. It can't. Why can't it multiply these two numbers must be the same? This one up here was a 2x3 matrix by a 3x4 matrix.

[00:08:59]That's the sizes. Two rows, rows, columns, rows, columns because these two numbers are the same. You can multiply.

[00:09:05]Also, something to note, the pros them notice. I could ask them, ask them if they notice the matrix will come out looking like a 2x4 matrix.

[00:09:14]Yeah. What about this last one? Can this one multiply? The last one? Yes or no?

[00:09:19]Can this multiply? Yes or no? It's a 2x1 matrix by a sorry a 1x 2 matrix by a 2x1 matrix. One row, two columns. The eight is a column and the five is a column by itself. This is one row. So one by two by two rows.

[00:09:39]Two. Yes. Yes. Yes. You can definitely multiply. Can definitely multiply. You could just write down the size like this. This is a This is a one by two trying to multiply by a 2x one. Are these two numbers the same? Yes. Strange enough, the answer is going to be the answer is going to just be one one answer.

[00:10:02]This is almost like you're working out the dot product kind of way. Um supposed to click no here, right? So we continue.

[00:10:10]Um so this is one of the type of multiplications you see in um Cxe all the time. A 2x2 matrix by 2x2 matrix. Of course it could multiply. This has two columns. This has two rows. So yes, you could go. So watch the flow down the row. So 6 will multiply by the 8. Then -5 will multiply by what? Cuz you're going down the row. But this could only deal with columns. So you have to pick the -6.

[00:10:35]And that's the first batch.

[00:10:38]If you want to go this row again, you'll have to go with the next back. You understand? Everybody take a chance to dance with everybody. But let's go with this bottom row. So the nine will go with the eight now. And the negative one will go with the what? So I went down the across the row. I'll go down the column with the -6. Are you vibing it?

[00:10:58]Are you vibing it?

[00:11:02]And then you do it again. The six will multiply with the back unit again with the back row. Now the -5 will multiply with the -2. And you have to work out those things. The 9 will multiply with the -4 and the -1 will multiply with the -2. Now if you do real plenty of this, you begin to see patterns cuz like if you watch here, you'll notice that 8 8 -6 -6 -4 -2. You see the pattern and then 65 65 91 9 Everybody had to take a chance with everybody. So you all will get to go go through it with yourself and press check. I'm not staying too long on this.

[00:11:45]You all will get to do it yourself, right? So look out. Maybe by midnight it will be up on the website. Um but definitely by the morning go and check matrix multiplication the tutorial and that and you could do it yourself. And as you do it and you write on your book and you do it for yourself and you move around the tiles, it will stick in your brain more. Some of you all need this.

[00:12:04]You don't need the teacher talking to you need to actually move move around things. All right. Um, you could always pinch the screen to zoom if it a little if you need glasses crew. 78 78 -4 - 34.

[00:12:16]Now, you could just put this in your calculator to get the answer if you're not seeing it. This is 6 * 8 is 48.

[00:12:24]They're kind of showing you here. 6 * 8 and then -5 * -6 is 30 positive 30. The negatives cancel. So 30 + 48 is how we get to 78.

[00:12:36]Seeing it pressing continue. Um what size will the answer be? So remember I told you the answer is going to be the outer things. So what size will the answer be if you multiply a 2x2 by a 2x 1? If I multiply a 2x two by a 2x one, what size will the answer be? The answer will be 2 by one. I tell them where they could find it.

[00:13:02]You all understand what happening there, right? So if I multiply, what is this? This this 138 by 53. This is a 2x2 matrix being multiplied by a two rows, one column, a 2x one. Because these two numbers are the same, it can multiply. These two tell you what the result is going to look like. It's going to look like a 2x1 matrix. So whatever we get here, we'll have one thing here in the end and one thing there in the end. That's what I mean. And if you multiply a 2x2 by a 2x2, obviously the answer will be 2x2.

[00:13:40]It only had twos down there, so it's going to be a 2 by two. All right, I hope everybody cooking. And last part, this is the last thing. And you all had to help me with this one. Everybody get ready to help me with this one. So I'm going to pick the four. Throw it in there. The three and the three. Then the five. And you have to slide down. Slide down. Slide across. Slide down. Nine with the -3.

[00:14:08]And then the five with this five. So what is the result going to be? actually have to type it this time. Somebody work it out. So you seen what it's showing me that each one is for, right? Seeing it.

[00:14:21]I'll take my time and make sure the word is pedagogical like it ordered in a way to kind of teach you by experimenting.

[00:14:30]So you're still not getting I'm not erasing the frustration by spelling it out for you, but you still getting a little better understanding of it. So everybody's saying that this is going to be -27. That's not correct. No. 27. You say 27.

[00:14:45]27. Why 27? 12 and 15. Yes. Correct.

[00:14:50]What is the next one going to be?

[00:14:56]9 by -3.

[00:15:01]9 by -3.

[00:15:08]Uncle Kwin. I didn't miss that comment.

[00:15:10]Uncle Gwin, Terry say he better. One, Terry would never say that and I would never say anything like that either. And and two, Terry is probably better. He's probably better. He's probably sharper in maths.

[00:15:24]It doesn't um a list of trying to pit maths teachers against each other. So 9 by -3 is -27 and -5 and -5 uh - 52 not positive 52 52. So now we could check that and you're supposed to get these things correct in the exam. If you understand that right understanding everybody get a good a good understanding.

[00:15:58]And now this one, this is actually a pretty long thing to do. But in the exam, what we what some of my students do is they just do the 5 by 1 7 byg -2.

[00:16:07]So 5 by 1 is ne5 and they just write5 one time. But I just have it here spelling it out for you. 5 by 1 -7 by two.

[00:16:17]And then I like to go to this part one time. But if you have a method that maybe you like to go across here one time, I like to go this part one time.

[00:16:25]Where am I? 9 by two. So I know I'm done with this column and I'm going to pass through this row and this column and then the bottom around this column. You catching the vibe is a is like a dance.

[00:16:35]It's like a dance. Don't mix up the dance and step on nobody toes. Right.

[00:16:40]And somehow you the only kind of dance you know is I don't know why them green thing jumping up there. I never tell them green thing to jump when I play this thing. You see you see that foolishness.

[00:16:53]Right. So we can check that so far. So we looking good so far. I just need to fill up these last slots. What are these last slots going to be?

[00:17:02]Somebody a calculator handle it.

[00:17:06]You're going to have -5 and -14. So -19 sounding good. -5 and -14. That sound like a negative and a negative 19 should drop inside there. What about this spot? So you see now they're highlighting what to do to get to this spot, right? -3 and 18. -3 and 18 is what? Put Leave that chair alone there.

[00:17:29]-3 and 18. So, man trying to take my chair on the down here. 15 -3 and 18. 15 across here now.

[00:17:43]Oh, here's where you want the 38.

[00:17:47]Here's where you want the 38. 10 7 fours are 28. And these double negatives, so they're positive. So 38 is fine. 38 is fine. Last row now, -3 by -2 is 6. So this is just a positive 6. And 9 by -4 is 36. So um 6 and - 36. So we're expecting a 30 there, right? Check. Oh, 6 94s - 36. Yeah. Oh, I said negative -30. Actually, I didn't put the negative.

[00:18:30]-30.

[00:18:31]Good.

[00:18:33]So, um it should be good. Everything looks like it's working. Yes, you can actually solve this on the calculator if you're struggling with your directed numbers, but I also have a directed tutorial on the website there that could help you get better in directed numbers.

[00:18:48]So, um, you'd find it on the website.

[00:18:50]Just search kwinspringer.com. You're not going to find this one yet. I just wanted to test it with you all to make sure nothing in I didn't miss anything.

[00:18:57]So, this one is going to be up. And if you're watching this in the morning, it's up. It's up. All right.

[00:19:03]Finish. Well done. And you can run it again. Run it again. But we not going to run that again. We done. We done for the hour day. We going to do some bearings.

[00:19:12]Everybody say bearings. Everybody say circle terms.

[00:19:16]Find the value of K O L given reasons for each step. K O L Whoa, whoa, whoa.

[00:19:31]They're making you work hard for K. Boy, I seen the way. But I find they make you work real hard for that K labor. You see you could find K.

[00:19:40]K.

[00:19:42]They make you pay the work for that K.

[00:19:44]No new friends were given up here and there's nothing new up here.

[00:19:50]Everything is on the diagram.

[00:19:54]So my class requested I touch on some circle theorems and some bearings. So here we are. Circle the terms and some bearings. So it's the vibe. We have 300 people on YouTube and I 100 people on Tik Tok. Tik Tok. How you feeling?

[00:20:07]Double tap.

[00:20:10]Find the value of angle K. giving reasons for each step of your work.

[00:20:20]I don't see no solid answers popping anywhere yet. Nobody holding on a solid answer. I see a 15. I see a 30. I see a 38. I see a 30. I see a 15. I see a 78.

[00:20:40]What? It had 10 likes. I doubt it at 10.

[00:20:42]10 likes and you press like. Double tap.

[00:20:45]Bring up the line. We have 76. We have 48. This one tough. This actually came two years ago. I think this is 2024. Uh Jan or something.

[00:20:56]We have a 90.

[00:20:58]People holding on at 90. It's not 90. I could I could see that it's not 90. It looking like it could be 90, but it's not.

[00:21:07]Wait, we have no solid answers. We have no solid answers. Are you want some clues? We looking for some clues.

[00:21:16]I want you all to see how I thinking through the question, right? Watch how I think through the question. What theorems do I have? You all remember the theorem thing that I did? I want to post it back up on the website. A lot of people starting to say 96 now. Y'all remember the theorem stuff that I did?

[00:21:33]What terms that you could see here? One time I could see a cyclic quadilateral.

[00:21:38]Can this help me? Not really. I could see the cyclic quadrilateral. What else I'm seeing? I'm seeing angle at the center, angle at the circumference.

[00:21:47]Everybody seeing these thems outside one this tangent here with the radius make a normal and then the last one is the alternate segment theorem and I think I've seen all these theorems inside here well except the outside point I've seen the alternate segment theorem I'm seeing the radius radius and that's the key. This all of a sudden that's supposed to light you up. This is our radius and this is our radius. That means one that's an isosles triangle.

[00:22:24]This is also 90 here.

[00:22:27]And if this is 48, what this could be to make the 19 away? Anybody starting to see the light? And then if you know this, don't you know this one time?

[00:22:38]Because it's a isosles. And then can't you not find that?

[00:22:44]I seen Rihanna big Brianna Cington one time. The radius and a tangent. The radius and a tangent form 90° at the point of tangency. That's a the term. So if this is 48, this here has to be 42.

[00:23:02]And if this is 42, this here is also 42.

[00:23:05]42 and 42 is 84. And if I minus 84 from all the angles cuz remember this had to be 42 cuz it's isoclesles in a triangle. I'll get 180 minus 84. And I want to say big congratulations to the 96 squad. 96 squad had it. 96 squad.

[00:23:28]Yes sir. So you have to show a lot of steps in this uh maybe three marks or two marks. Two marks. The next part was angle L MN. Lemon LMA LN. So what is LMN going to be? L MN. LMN is one thing. I already pointed it out earlier. LN lifetime.

[00:23:52]LN L MN.

[00:24:14]I was actually watching the round thing for LMD.

[00:24:20]I watching I was watching LMT. We want LMN. LMN is over here.

[00:24:28]That's LN LN.

[00:24:32]So what we seen for LMN? So I pointed it out earlier. This is a cyclic quadrilateral. It's a it's a angle in a cyclic quadrilateral. So I could probably cook up something here, man.

[00:24:44]I'm seeing a couple ways to get to LN.

[00:24:47]Here's one of the ways that I'm seeing.

[00:24:49]If this is 96, this must be half of 96.

[00:24:52]Half of 96 is now 48 because angle at the center is twice the angle at the circumference from the common chord in the same segment. And don't you also know that this is 56? How do we know that this is 56? Alternate segment theorem.

[00:25:09]And 56 and 488 is 104 104 degrees. And I've seen a lot of people cooking up the 144 in the chat.

[00:25:20]But some of you all cook up the 104 a different way, which is fine. You were like, I'm seeing that this y'all spotted that this has to be 34 because this is another 90 here.

[00:25:32]And then you added the 34 and the 42.

[00:25:35]Isn't that what you did? 34 and 42 must add up to the opposite angle. Something like that you all did element. Yeah, opposite angle. So 34 and 42 is what?

[00:25:47]76. So it missing 104 on that side.

[00:25:50]Supplementary. So I'm seeing a couple of you all did that too. Usually there's a couple ways you could get to the answer.

[00:25:56]Is there any other way? That's very obvious. Not really seen any very obvious way. So yeah, we have this one as 104. Now don't forget you'll have to write your reasoning and all of that. We just practicing. Clo. We have to find K.

[00:26:10]Clo K.

[00:26:13]I already found the KO. KO is 42.

[00:26:17]Maybe there was another way to get to that 96 dead.

[00:26:23]Yeah. Um I could have made I could have doubled the 48 and then half the 48. So opposite angle. Maybe they expecting me to do a 48 48. Half of um double the 48 and get the 96. Maybe that's how they wanted me to get a 96. So there's two ways to get the 96 at first. Um but yeah, I already got that clue is 40.

[00:26:44]What? I forget. Yes. 42. 42. Zion. Why you knocking that boy? 42.

[00:26:50]MLK. Martin Luther King.

[00:26:56]MLK class. We was joking. ML is some kind of AI. MLK.

[00:27:02]ML key. So MLK key.

[00:27:08]Yeah, we could cook up an ML key. But is there an easier way to get to MLK key?

[00:27:13]Boy, I not seen a particularly easy way to get my to MLK. You really need that 12.

[00:27:24]That's why they give you that 12. You really need that 12 cuz I need to take away the 12 from this to get this angle here.

[00:27:32]So, I don't think I could get MLK without considering the 12.

[00:27:43]kind of hard for me to get MLK without considering it's 12. 12 from 42 would be what? 30. So knowing that this is 30 and this is 48. Now I could very quickly get MLK.

[00:27:55]Missing angle in the triangle. 30 and 48 is 78. So MLK would be uh one is this 30 for sure. 30 and yeah 30 and 42. 78. So MLK is going to be the 180 angle minus the 78 which is 102. So MLK is 102. What do you think about our circle terms? That's a pretty challenged one.

[00:28:20]Challenging one, right? Oh, there's a there's a last bit here. Kum kum knm very close to PNM.

[00:28:29]KN&N we have to figure out KN&N as well.

[00:28:31]Well, once I figure out this is 102, in comes this with an I78 and excite quadrilateral pops up again.

[00:28:40]So, parts easy, parts hard. This was a particularly challenging one. If I were you, I'd go and strike a few right now if you took your time on this one. A lot of people struggle to get the first one.

[00:28:51]Remember how long it take for people to start a zeroing on the 96? So, I think I'll catch a one day. I catch a lady. Um this turned out to be 78. Earlier we on we were doing some matrices. So if you missed that you can always watch it back afterwards. And let's go to this bearings question. How long are we here?

[00:29:08]We already here for half an hour. So I could still do a next question afterwards. Right. Efj by the way we coming to end. I'll have one more session when Wednesday and hopefully one session on Thursday as well. And after that, I'll be focusing on sharpening of the website, polishing of the Discord, doing certain things there. Um because I really need the late night time to do that. And then Monday, I have a 12-hour crash course. So, um make the investment and jump out in that 12-hour crash course that I have on Monday. I want as many people as possible there. Um, we'll be going most likely from 8:00 a.m. to 8:00 p.m. You have to WhatsApp this number 3101306 for the area code for Trinidad plus 1868 and jump in. Anybody here from the student hub in Tik Tok or WhatsApp and they can testify that um good things be happening in the student hub. You can also use this to register for any other crash course you want to pop into.

[00:30:05]Right.

[00:30:07]Um after that 12 hour crash course after that I have some more two cars on physics physics 12 and admats to do real pieces real piece E FG and H have four points on the level ground the diagram below gives information on the distances and angles between the points right so it's it's not really a bearings Z question oh we do have not we do have not so should the value of X is 29.5 five.

[00:30:42]So, we're going to use to find X. This is one of the worst ones. This is one of the worst situations you could get.

[00:30:50]This is one of the worst the the ugliest situations that you can get in a bearing situation bearings question.

[00:30:58]What are we going to use to find X? A theorem. What term? What term you're talking about? What are we going to use to find X?

[00:31:08]Other than Malik, what term what's what rule are we going to use to find X? I'm going to use the cosine rule. This is actually a version of the guy. Remember I told you all about the guy, the head, angle is the head holding up the stick. And we need to find the length of the stick. Except this is the worst version. This is where you actually know the length of the stick.

[00:31:30]So this is the reverse go side roll.

[00:31:33]This happens. Listen listen listen to send the discord link again. All right. I'm going send the discord link for the people on Tik Tok. Somebody telling me on Tik Tok again. The link right here is working. What going on with you? You get banned from discord.

[00:31:49]The link right there. You could go on my website and click it. Is that eternal?

[00:31:53]Your comment wasn't posted because of this live settings my friend. I can't even send the link there. Are you trying to get me banned from?

[00:32:07]I just share the numbers there. They didn't even post the numbers. Tik Tok real grimy when it come to sharing things that not on their platform.

[00:32:17]You don't know Tik Tok hate me already, but I share it on YouTube. But you could come and see on YouTube.

[00:32:23]Um, tell me if you seen the link train up on YouTube. Yeah. Yeah. So, this is the worst version of the cosine rule.

[00:32:29]Just to reiterate for those of you all who reach that point in studying yet is the cosine rule really works like this.

[00:32:36]I'll kind of put it in the way that it almost always shows up in the exam. Um, you have to find the value of this this side and usually you're given this side like this side might be given as as 100.

[00:32:50]This thing too skinny. Let me try again.

[00:32:53]So, you have some kind of triangle.

[00:32:54]These things involve triangles non-right angle triangles when they when they come in specialized they could use another right angle triangles but you wouldn't because you could use pythagoras and so you're trying to find the value of this side but you usually know this side you might know this is 120 km and you might know this is 100 km and you would know this angle this angle might be let's say 70° so this is nice this is the usual form of the cosine rule. And in this form, you call this angle capital A, this common A, this B, this C. And the cos of A 2 is equal to B 2 + C^ 2 - 2 B C of A and you will figure out A. A is where you're trying to figure out. Now another situation that you can use the cosine rule is if you get the same setup but they don't give you the angle boy.

[00:33:56]So like they they give you the same setup 120 km 100 km or whatever and then they tell you hey I also giving you this 110 km and now you had to figure out the angle the angle is the unknown. Well you could set up the same cosine rule chat are you with me? B^ 2 + C^ 2 - 2 B C cos of A. But this time the unknown is this.

[00:34:23]You understand? And I'm going to do it in the question now and you'll see how is unravel. So that's what this question has. If you watch it carefully, you would see that triangle with X in it. We actually have the sides of the triangle known, but we don't know what X is. So we have the three. So that's the dead giveaway. I had to use the cosine rule in reverse. Dead giveaway. Dead giveaway. So you're going to say a^2 is equal to b^2 + c^ 2 - 2 b c cos a.

[00:34:55]But you only say this if you like draw it over and you rename the stuff like I'm drawing it over here. I'm saying 5.31x um 6.9 and I'm kind of renaming. I want to rename this capital a comma a b c. So I have my diagram there. Instead of using gh I always talk about that, right? You could just rename it over. So you could use your format here.

[00:35:21]Yes, you'll have to transpose the formula. So you're doing any YouTube crash course. So what you think this thing doing every night is you doing work every night. So you doing 12 crash course this year? Yes, it's happening this year. WhatsApp the number to to pop in. Jump in.

[00:35:37]Is Monday. Don't wait too long. next week Monday. So, we had to register for that now. Now, like tomorrow. Um, so let's put in all the things we know and the things we don't know. So, a squ would be 6.9 squared. B 2 will be let's put that as 5.3 2 + c² is 11 2 - 2 by 5.3 by 11 cost of the angle that we trying to figure out that bad boy there. We're trying to figure out him. So, you're going to bring across all these things.

[00:36:09]Somebody tell me what they are. See, I remember I delete my calculator.

[00:36:14]So, somebody had to tell me what 6.9^ 2 minus 5.3^ 2 and then you'll have to minus 11^ 2 and then we'll end up dividing.

[00:36:25]So, this will turn into a negative number, right?

[00:36:29]This will turn into a negative number, but you'll end up dividing back by -2 5.3 by 11. So put this thing in your calculator and tell me what you get.

[00:36:41]So somebody tell me going to work out to be 29°. Uh Malik is saying it not supposed it not it's supposed to be negative. It get a negative number.

[00:36:50]Okay. So the degrees was X is X's. No X is an acute angle. So it's supposed to be positive.

[00:37:01]Supposed to be positive.

[00:37:04]All right. You just tell me what the top is. Tell me what the whole thing is.

[00:37:08]You're getting -101 over -48. Something like that you're getting.

[00:37:14]Why divide?

[00:37:21]All right. I think I need to go and bring back my calculator. I need not not because I trust all you.

[00:37:26]Although somebody has been have been known to lead me down the wrong road already, but because I want to show somebody in the chat how we doing this.

[00:37:36]I want to show somebody in the chat how we doing this.

[00:37:39]Secondly, my brother bring it up for you.

[00:37:44]Try your best and behave yourself this round. Let the people like you.

[00:37:49]No, I want to continue with my current bootleg version. Good. Nice.

[00:37:56]That's not I'm make sure I'm right.

[00:37:58]Good.

[00:38:01]Watch carefully. Now, now usually I'm going tell usually what I just usually don't do it like this. Usually I work out this part here first just for kicks.

[00:38:17]So like I would be like 6.9 squared.

[00:38:20]Get that.

[00:38:22]Yuck. get that 47.61 the number I was just looking too big for 47.61 and get this one time as a number. Are you catch my drift? So if you're not seeing all the big jumble that look like a good thing you could do there.

[00:38:41]So work out this part. So 149.09 that making sense everybody?

[00:38:47]Minus and I could work out this piece here. this little bit here. 1* 2 2 5.3 by 11.

[00:39:00]Are we cooking ladies and gents? So that's 1116.6 cos a. So then you you're seeing the numbers you're seeing what happened there. I substituted that. This is that.

[00:39:13]Now this is this this bit here is that and this bit here is that. So you can think of these like normal numbers 3 2 - 2x. So you have to bring across this then you'll get 47.61 -149.09.

[00:39:31]You understand? And you'll get something there. But I I'm already seeing in the future that I'll have -16.6 cos a here. So why not just bring across that one time with the minus sign and put cost a there. So I'll have minus16.6 when I divide. chat. We cooking now. Are we cooking? Everybody follow the movements.

[00:39:54]So now Clyde um I I am not known for cussing 47.61 speed live streaming 149.09.

[00:40:10]I can't remember if that was 149.09 it was. and then uh -116.6.

[00:40:20]So I can put that straight in my calculator and get this number there. So I get 2537 2915 2537 2915.

[00:40:33]That's what the C of A is. Oh yeah, cuz I say C A. I think I catch the joke there. Sorry I take so long to catch the joke. So a is the c inverse of 2537 over 2915. You got to bring across the cen inverse.

[00:40:51]Oh yeah. So c inverse of answer should give me the answer or c inverse I could write out the whole fraction if I feel in right outish. And the person was correct. It is 29.5.

[00:41:03]Hey, they wanted us to show that it was show that question equal 29.5° to one decimal place. So we that feel real good because since I show that question we get the answer out that we are supposed to show what was to be shown has been shown them one time QED on that um I'm not really feeling to do my next question. So vertical tower it's kind of late I start late today is constructed at the point G and is pivoted to the ground at the point E F and H. So GT, somebody say Georgetown.

[00:41:42]Georgetown. Georgetown. So GT is constructed at the point G. So this is T. This is G. And it's pivoted to the ground at points E F.

[00:41:53]They give me a diagram here.

[00:41:57]However, I feel this is what I meant. E F H.

[00:42:05]That's what I mean. I think it's in the same plane.

[00:42:14]the angle of elevation at the top of the tower from F. So, E F H. I'm hoping I do the right thing here cuz I don't know if they give me a diagram and I the diagram had a diagram, sir. Answer my question. All right, let me go and talk to see what my boss before I get fired from this YouTube box. Sorry, I not seen your question scrolling and I not seen your name. So um should I just ask question again? I might have spotted them. Um yeah it's one tower but they say it's pivoted to the ground E F and H using pieces of wire. So I think like it's one tower and it pivoted to the ground. I think that what they mean. I feel I feel like um I need a diagram in this and I didn't snipe the diagram.

[00:43:08]Play myself here. I play myself.

[00:43:12]Was there a diagram given for this question?

[00:43:24]Not find any finding the question or you could tell me if this doesn't have a diagram. What was the length of the wire used to secure point the tot? Okay.

[00:43:31]Well, we could work out anyway. The angle of elevation at F. So angle of elevation is the angle of the horizontal. So this is 31° and this will join up here like this. So we cooking and what is the length of wire I use?

[00:43:51]No, I need to know I need to see dimensions. I need to see dimensions. So I play myself here. I don't have the um I need a a dimension here. I need a dimension here. So GT is pivoted to what is the link? I can't work out anything.

[00:44:05]I only have one piece of information. So it was it was messed up. I'm missing some number there. So sorry about that.

[00:44:13]Let's go do this one. So we can do I can make it up with this question. Right.

[00:44:18]And you take the angle of elevation that real easy thing to py theorem. Okay. Go look up angle of elevation for in spring channel. The line DCE is a tangent to the to the circle angle AC is 48 and OCB is 26. Good.

[00:44:37]So this must let's identify all the terums we seen here since you all are ter bosses now.

[00:44:45]Feeling real hungry boy. Hungry again boy. I wonder if some late night doubles or something I could go and check out now boy.

[00:44:56]48.

[00:44:59]This is a tangent and a chord alternate segment termal. You seen them also seen the arrow head center. Boom. What else you seeing? That's about it. Not much.

[00:45:11]It triangles. We seen the triangles. We seen the tangent. Oh. Or I seen a radius and a tangent. So that mean this is 90 and this is 90.

[00:45:21]That's the three terms there. the arrow head, the alternate segment term with this and that and also the radius and the tangent. Watch out for that one. That one is real crack the puzzle sometimes. Angle ABC. Well, let's start off with this one time and I already done prep for them. I already know that that's going to be a 48.

[00:45:41]That's just a straight 48. A B C. You all catch how that is 48. The angle the angle between a tangent and a chord is equal to the angle. So that's this angle is 48 is equal to the angle in the triangle in the alternate segment. So that triangle that touches the circumference in the alternate segment is 48. Who else thinks they asking me here boy? AOC AOC um they are American politician kind of we don't say nothing 48 48 multiply by 2 48 multiply by 2 is what 48 multiply by two cuz that will be twice the amount and 96 right 96 are we cooking chat or I alone cooking here you cooking too you all watch the video that I did on circle time so this is feeling good for you all BCD ED B C D Well, this had to add up to 90.

[00:46:40]So, I know there going to be four um four make 30. So, 64 64° 64°. We just walking through this.

[00:46:49]There's a walk in the park. This one is a walk in the park. Back. Let's go and find the size of back. That's this guy here. Well, that's our next alternate segment term I'm showing up here, ladies and gentlemen. So, this will be 64.

[00:47:01]angle between the tangent and the chord is equal to the angle in the triangle in the alternate segment. So BC is also 64.

[00:47:09]More cooking again.

[00:47:13]Uh O A O A All right. They kind of slow me down.

[00:47:19]They slow me down. Why? Slow me down.

[00:47:22]So O A is this angle here. And I know that this is a isoclesles triangle.

[00:47:30]We use this 26 yet.

[00:47:34]Oh yeah. Take to minus. Oh yeah. So this is 96.

[00:47:40]So then what these two are to be? These two here add up to 180. Now so if I take away the 180 and I take away the 96, how much I get?

[00:47:54]getting 84 84 and then I divided by two. Hey, we got a 42 thing show up already for the 19th. See, you're repeating your numbers, big dog.

[00:48:05]So, there is 42. So, this is 42. Now, OAC is 42 and O A O A A this little sliver here. Well, I just I just was running out of things to say. So, they tell you do O A and they don't do that these days. It does never run a lot of things to say. B A C. We already have 64. We already have 42. So just add a little two, a little 22 on and we cook in there. 22.

[00:48:32]Chat, are you cooking? Ladies and gents, Chav, you cooking? Yes, sir.

[00:48:41]Chavian say hello to the people.

[00:48:44]Just just wave at them so All right. So this is this is 22 man down here taking the max too.

[00:48:58]Sit down here taking a chavy is how old are you? 10. 10. You just turned 10.

[00:49:07]>> Almost 10.

[00:49:08]>> Almost 10.

[00:49:11]He's almost 10. But he's good. He's good in maths. He's doing like form one level match.

[00:49:17]All right. I had to zoom in for this.

[00:49:19]No, no, no, no. We pulling up the handbrekes. I going to take a vote. Are you good here or are you want to see that question? We good here. Jump into that question.

[00:49:37]We good. Lovely. Say we good. Brat say jump in. Ra Queen just share the live.

[00:49:42]Big up Rave Queen. Shy share the live.

[00:49:44]Niki say jump in on the kiss. Let somebody say jump in on YouTube. Do the question. Do the question. Real people saying jump in boy. Oh like like exam is in a couple of weeks. So normally people just be like we good sir. Yeah we real good. Copy the diagram about on your diagram. Label the angles that should bearing 25 and 80.

[00:50:05]P is on a bearing of 25 from O. On a bearing is this a hurricane tracking station. P from O 25. So, I'm going to put 25 from O right there. I want to put a zero to write 025. We We ain't trying to lose no points here. And OP is 400. So, this is 400 kilometers, right?

[00:50:33]OP OP is 400. So, this is 400 right here.

[00:50:39]What else? Q is on a bearing of 80.

[00:50:43]Q is on a bearing of 80 from P. So this is 80 here. Was that where everybody was thinking to put those things? I hope that's where I was thinking to put those things.

[00:50:57]Good. Now calculate OPQ.

[00:51:00]OPQ. OPQ. OPQ is this angle right here.

[00:51:05]So we're going to use um we could use two things. If you understand back bearings, you could use back bearings here. This was 025. I just want to write it properly like 025 25 and 80. You'll get this little piece here so you know. And then you subtract the 80 from that. Subtract 80 from 225 and you'll get from 205 and you'll get the answer.

[00:51:33]There's another way to do it. You you could use there's like three main ways to to lock down this question. If you watch my videos from earlier in YouTube, one of the ways that I would do this would be to work out this angle as an alternate angle with this. So that's 25 and then add 180 here. So 180 and 25 and you get the answer.

[00:51:58]I'm sorry. Um and then you subtract 80 from that. Um the way that I push students to do it now is co interior. So if you if you know say co interior co interior means that this angle is co with this angle is like the u shape. I went through this already here people go back and watch the circle theorems video. So that's co interior angles there. And that means that these angles must add up to 180.

[00:52:26]So that means that this angle here is 180 minus 25 which will be 155. So 155 80 and this last bit here is 360. So that's one of the stronger ways to approach the question.

[00:52:41]One of the stronger ways to approach this style of question and everybody's telling me that it's going to be what?

[00:52:46]So it's 155 and 80 53 1 2 35. So 360us 235 25 125. So you get 125 here. That's how the cookie crumbles.

[00:53:04]Cool.

[00:53:06]And then what's next? Do we have the guy with the hands? Do we have another length? PQ is PQ is 700. So this is a classic bearings. Classic. You're hoping to get thing like this once they overdo it. This is this there's like about five or six questions like this in the last 15 years. Just like this same old setup.

[00:53:25]The guy with his sticks. We got the hand holding up the stick and we had to find OQ. I don't need to watch the next part.

[00:53:30]We're going to have to find OQ for sure.

[00:53:35]the bearing um the length OQ and then the bearing of Q from all so building up here really feeling to do this easy thing and all right OQ so we're going to draw this boom bang bang uh I'm doing it this method oh let me do the um normal naming method for the bosses them right so who are custom with these cosine rule and comfortable at it um we could use normal Well, you can just use the same OPQ names instead of drawing over the triangle if you're feeling like you want to do that, right?

[00:54:10]So, OQ 2 is equal to this OP ^ 2 plus PQ ^ 2 minus 2 OP PQ um let's put this in brackets uh cos of angle O P Q. Then we just substitute like rain.

[00:54:35]So we're still trying to get OQ ^ 2.

[00:54:38]OP is 400 squar plus PQ 2 is 700 squar - 2 by 400 by 700 cost of 125. So you want to put this whole thing straight into your calculator and tell me what you get. Try and agree on something, right? Don't tell me the final answer yet cuz I'll still need to get the square root of what they tell me is and then get the final answer, right? And I'll be kilometers. But tell me what's supposed to go here first. Chat, everybody do it in your calculator and see how they get it. And then you put it back here and then we get your answer.

[00:55:20]Chat, talk to me. That's 125. You all see all the substitutions, right? kind of clearly labeled waiting on something here from the bosses 985 is I tell her they don't give me the answers prunella you gave me the answer saying is 985 to the nearest kilometer I wanted the number here you get prunella yeah Joy boy I was busy I And the same son who right here waving to teach him some things on the keyboard and then I come straight back and it take kind of long to I start late today.

[00:56:10]So nobody want to tell me was the previous thing m.

[00:56:14]So wait a 985.5 and then it get round it to 98.5 985. Thanks boy jam jam jam to whatever your name is. 971202.8 is what it's saying. So 971202.8.

[00:56:37]Oh, what going on?

[00:56:47]Malik Malik had paid before. No, Malik didn't pay it. I feel like going and check this and I just have to worry.

[00:56:53]400^ 2 + 700^ 2 - 2 by 400 by 700 cost of what it was 125.

[00:57:13]Yeah, she was correct. And then you get the square root of answer uh S.4 my brother 49. If I was rounding off here, it would be four 58.5. But if I rounding off here, it's 985. So, so they're correct with the 985. 985 km is the way.

[00:57:31]Cool. And the bearing of Q from O, this is the last thing for today. The bearing of Q from O. So, I'm looking at this number here cuz I need to get this number.

[00:57:42]Bearing of Q from O. So, that'll be a little traumatic because I had to pull out a little sign out the hat here.

[00:57:49]Can't wait.

[00:57:55]Yeah. Wait. Jude Caribbean map is um Jia.

[00:58:00]So I had to I had to use a little sign to pull this one out the hat.

[00:58:06]They catch it.

[00:58:08]This would map with the 700 and this 125 will map with this 985.496.

[00:58:18]using a more accurate value. Not too accurate, but good enough. So the sign rule says that if I call this A, well, let me call this one A and I call this common A, that's how the sides go.

[00:58:30]Capital B, common B. That the sign of A over common A is equal to the S of B over common B. Now, the reason I put S of A on top is because I'm looking for A.

[00:58:45]because I'm looking for a.

[00:58:52]I just watching the chat here. Good. So, the sign of a over 700 is equal to the s of 125 over 985.496.

[00:59:07]Then I will bring over that 700. S of a is equal to the s of 125 985.496 * 700. So a is equal to the sin inverse of sine of 125 over 985.496 * 700.

[00:59:30]I just put the whole thing in the calculator and done cuz you on top of the world.

[00:59:36]That's called the sign rule, ladies and gents. And that's how it's done. You can re refresh yourself on the sign rule.

[00:59:43]Somebody say nia by the boss. Boss lady, where's the order?

[00:59:58]We do the right thing out here. Time.

[01:00:02]I think that is later later will be greater 35.6 all the way the bearing that's not the answer can't get them that that's not the answer let's say 35 they didn't tell me what it to the nearest let's say 35 6° so if this is 35.6° the bearing itself is going to be the 25 plus the 35.6 6 catcha 6 5 and 5 is 10 1 60.6 so 60.6 six. Now, if it's a three three figure bearing, it's best to write 0 6 0°. That's the best way to write it. 2 1°ree cooking. Why? Because the bearing is taken from the north. The bearing is taken from the north. So, we just going through one thing to find out that this was 35.6. But the bearing is taken from the north and goes until it hits the line that connects the two points that you're trying. So we want the bearing of Q from O. So we're going to use the summation the sum of 25 and the 35.6 to get this whole angle here. That is be the cooking um was it 0.1 35.6 six to the nearest oh sorry yeah.1 I don't know how to I don't know how to approximate one this will carry across to one right approximately to the 61 to the nearest degree now we cooking ladies and gentlemen as a quick run of circle terms and bearings and also a little touch of matrices that brings our hour to end for tonight I will see you tomorrow night where hopefully tomorrow night there is a chance that tomorrow night will be late Wednesday and all Every meeting is go.

[01:01:56]I'm hoping that we could just vibe tomorrow and do some random questions and then Thursday I might do something a little more solid. Um Wednesday I wanted to try and get in another subject here but we'll see. Love and blessings.

[01:02:11]Love and blessings ladies and gents.

[01:02:13]Take it easy.

[01:02:15]Tik Tok. I don't go check out the website. Go check out the student of Discord. Check my last video on Tik Tok and on Instagram.

[01:02:31]Do we need to bring our paper for CXE?

[01:02:34]No. No, you don't. No, you can't. You can't walk into the exam with any paper.

[01:02:41]Story. Stories.