PDTV MATHEMATICS SHOW-WITH MR. THOMPSON, May, 23,2026

Added: 2026-05-25

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[00:01:02]Hello. Hello guys. Welcome to another PDTV mathematics session here at 1 to 2 p.m. every Saturday.

[00:01:18]All right, guys. This is the best place to be as a high school student on a Saturday.

[00:01:26]>> Let me fix.

[00:01:43]>> I'm hearing an echo interference.

[00:01:49]message this.

[00:01:57]All right, guys. So, let me know how the audio is going, guys. Audio check. Audio check. Let me see what's happening here. Audio check.

[00:02:11]Yeah, YouTube people, let me see what's going on over YouTube side.

[00:02:20]Oh, hold on.

[00:02:26]YouTube audio check, guys. Let's check to see what's happening. Are you ready to level up your future? Every Saturday, PDTV brings you maths class on PDTV YouTube channel, the place where knowledge meets opportunity.

[00:02:40]Level up your brain.

[00:02:47]>> How do you check guys? I'm getting some guys. I'm getting some >> negative interference.

[00:02:54]>> Person on YouTube. Let me >> let me know how the audio is going.

[00:03:02]YouTube people, audio test, please and thanks.

[00:03:07]Testing, testing, audio check.

[00:03:16]All right, good, good. Thank you, YouTube. All right, let's do this again.

[00:03:22]All right, perfect. So, we're back on track right now.

[00:03:26]So, I'll ask them to send the link in the YouTube stream chat. All right, guys. So YouTube people let me know where you are joining from and your name right where you're joining from and your name for YouTube guys please.

[00:03:48]And remember the emojis are what we use to help me to understand if my audio or visual is on point.

[00:04:06]All right, let me check with the link for the for the meat.

[00:04:11]All right, let me check them.

[00:04:23]All right, guys. Yeah, just ask them to send the link in the the stream chat.

[00:04:28]All right, one final check for the audio. Audio check, please. And thanks. from St. Thomas. Amazing.

[00:04:37]From St. Thomas.

[00:04:41]Welcome from St. Thomas, guys.

[00:04:46]Anybody else? Any other parish?

[00:04:52]Any other parish joining us today?

[00:04:56]Do we have anyone from the United States, UK, Canada? because that's how far we stretch the the influence on a Saturday at this time right across the diaspora.

[00:05:09]All right, guys. I think I know where the issue is.

[00:05:14]All right, let me see.

[00:05:17]Teacher, send the link. Hold on. I I just asked them to send it just now.

[00:05:21]Sorry about that.

[00:05:25]Sorry about that, guys.

[00:05:29]Let me make a next check.

[00:05:34]We have him some.

[00:05:36]Yeah, I just asked them to send the link, guys. So, please be a little bit patient for a couple of minutes, please.

[00:05:42]All right. So, I'm not in control of the link. So, I don't have the admin capabilities to add the link to the to our chat, right? So, I just asked them back in studio to ensure that the link is up and running.

[00:05:57]Guys, remember please share the YouTube link to families and friends who can benefit from this session.

[00:06:08]All right, so we're going to start things off right now. 206.

[00:06:12]So just doing a quick recap of what we covered last week, especially for persons who were not on the show. All right. So, we covered trigonometric ratios and this is a little bit more higher than the basic Pythagoras theorem that we covered a few weeks ago.

[00:06:36]So, the other step to this is trigonometric ratios that we use to solve missing sides and missing angles of right angle triangles.

[00:06:48]All right, YouTube. Let me see some emojis in the YouTube chat. That is how I know that you're getting good reception in terms of my audio and my visual.

[00:07:01]All right, let's see the emojis for YouTube guys. If I get 50 emojis right now, I start the session right away. 50 emojis. It doesn't matter what it is. Once it's clean emoji, 50 emoji and then we kick off things right now. Let's go. Let's see the emojis coming in, guys. The emojis are free. So start tap up the phone and send the emojis them.

[00:07:22]All right, perfect. Somebody said remember to take screenshot. That's important especially what is on screen right now. These are the three trigonometric ratios.

[00:07:34]You'll use this even up to the college level. Let's go guys. Send up the emojis. Let's see the emojis in the chat guys. Let's like up the the stream and get things done guys. want say 50 emoji right now start the teaching.

[00:07:53]Come on man. The emojis are free guys.

[00:07:55]That's how you engage with the with the thing.

[00:08:00]Let's see who is here.

[00:08:03]Yeah man. Let's see the emojis coming in man. Let's go guys.

[00:08:08]Emojis are free.

[00:08:11]All right. So on screen, I'm going request the the link one more time. Yes, I can.

[00:08:49]All right, guys. We are back again. Uh, just ask them for the for the All right, guys. In the meantime, let's work with the YouTube for now. I requested the producer to send the link in the chat, but I guess probably he doesn't. a message about in the meantime, let's get things going. All right, how are you? All right, I just tell him to send the link. So, within a a minute or so, it's going to be sent. So, on screen guys, we have the three basic trigonometric ratios. And as we covered in previous classes, these three trigonometric ratios are only used with right angle triangles.

[00:09:45]All right, right angle triangle. If it's not a right angle triangle, if it's not a right angle triangle, guys, where's my audio? I keep getting some negative interferences in the background.

[00:10:01]All right. So if the triangle is not a right triangle, we will not apply the basic trigonometric ratios guys. The link is in the stream chat.

[00:10:13]Link is just was just sent in the stream chat guys. So, persons who want to join the Google Meet session, just click the link and give me a couple of seconds to get you guys in. And please, if you join the Google Meet session, just don't come in and sit back and be a spectator. Please interact and ask questions.

[00:10:38]That's how you can get clear understanding of what's going on. All right. So, without further ado, guys. So three basic trigonometric ratios.

[00:10:47]So we have the first one has been sign of us in the class.

[00:10:57]Come on don't watch the amount in the class man. The the number is going to fly.

[00:11:03]Number is going to fly right when we just starting know. So sine that we have right here and the ratio for the sine theta is actually opposite over hypotenuse.

[00:11:19]Cosine cos theta equ= adjacent over hypotenuse.

[00:11:24]And for the tangent tan theta equal opposite over adjacent. And remember this little symbol here, it means angle.

[00:11:37]It's pronounced as theta. But whenever we refer to this, we are speaking about the angle.

[00:11:42]And that's the same angle that's in the triangle right here. So whenever I write an angle inside, we're referring to that symbol.

[00:11:54]All right? And we would have covered these two questions last week. So we're not going to work these two questions again and we would have covered these questions as well. So YouTube, you're going to tell me which num. So we're going to choose two from the questions on screen. So I have four questions and as a part of the recap, which two questions should I reinforce?

[00:12:25]So come on YouTube space. Which two question should I reinforce? So I have 1 2 3 and four.

[00:12:32]Right where it says find the length of the side marked X. So 1 2 3 and four.

[00:12:37]Which two questions should I cover?

[00:12:43]Let's go YouTube.

[00:12:45]Which two questions should I cover?

[00:12:51]Let's check the the waiting area. All right. Pool guest.

[00:12:56]Let me see them. Admit them already.

[00:13:01]Let me see who is inside now. So >> sir, >> all right. No problem.

[00:13:10]Back to our session, guys. So YouTube people or Google Meet, which two question should I answer? Two and four.

[00:13:17]All right, let's move to two and four.

[00:13:19]This is just kind of a a wrapping up type of recap thing before we move on to a little bit more technical sort of stuff. So two and four. All right. So what's the first first thing that we did whenever we were looking on solving right triangles guys? What's the first thing that we need to do?

[00:13:47]First thing that we need to do before we even start to solve these type of problems.

[00:13:52]So I'm doing two and four according to let me see let's go guys YouTube type it in the in the the chat what's the first thing that we do to the triangles whenever we are working with trigonometric ratios.

[00:14:15]Come on YouTube and stop give answer them so quick.

[00:14:20]What do we need to do?

[00:14:23]One week ago I forget already.

[00:14:28]Let me go in a Google Meet and see what going on in there.

[00:14:33]Let's see Google Meet. I'm coming in. All right.

[00:14:39]Don't mind the infinite screen that you see here. I'm going to show a different tab. That's why we have it like that.

[00:14:46]All right. Google meet people.

[00:14:49]Where are we?

[00:14:52]All right. So, Nerly Green and uh Sheniqua Corinthian.

[00:15:02]Hope I get those pronunciations correct.

[00:15:05]What's the first thing that we need to do to the triangle whenever we are working with trigonometric ratios?

[00:15:14]Guys, I tell us not to come on and be any spectators in the Google meet session, you know, cuz it's to interact YouTube space probably a no good or something probably a hot know last week.

[00:15:39]But here do it.

[00:15:44]Remember when come off of this? Nobody nobody said go back over hit.

[00:15:49]I have 20 people.

[00:15:52]All right. So the first thing that we do the person who said two and four. Thank you. What's the first thing that we do with these triangles so that we can know what trigger ratio to use?

[00:16:06]I tell you last time I tell my move. So if you're looking at number two, first thing we need to do is to label the sides.

[00:16:18]So this is 60° as the angle here. So if the angle is here, then this side here.

[00:16:30]>> Hi sir, >> that's the opposite.

[00:16:33]>> Hi sir, your is good.

[00:16:36]Hello.

[00:16:42]>> What's that?

[00:16:45]>> Audience is good.

[00:16:48]>> Okay. The audio is good.

[00:16:52]>> All right. Thank you. Remember if you're on Google Meet, do not listen to the YouTube. All right.

[00:16:58]Going to mix you up and it sound crazy.

[00:17:03]So if you're on Google Meet only listen to Google Meet audio.

[00:17:09]>> Okay.

[00:17:10]>> All right. So we label the first side.

[00:17:16]No matter I'm just going to do number two if not interaction question.

[00:17:29]>> All right. So this now is opposite.

[00:17:34]All right. And the longest side here that is facing the angle symbol or the right angle symbol. That's the hypotenuse.

[00:17:46]All right. And by default, what's the third side called? YouTube. What's the third side called? I have opposite. I have the hypotenuse.

[00:17:55]What's this side called? The 15.

[00:18:00]tube asleep. What's this side called? 15 YouTube people where sleep carry on.

[00:18:20]All right. So, this is the adjacent side right here.

[00:18:26]And uh no need to identify which trigonometric ratio you're going to use because you have s tan cos you have to choose one. So in this problem you given 15 cm for the adjacent side and you're being asked to find the opposite side which is x cm.

[00:18:54]The hypotenuse didn't give us a value.

[00:18:58]So we're not going to look on the hypotenuse side right here.

[00:19:02]Right? So in terms of our solution, we have opposite and adjacent. So that is the tangent ratio. So tan theta equal opposite over adjacent.

[00:19:22]So once you get the opposite side and you're asked to find the adjacent then we're using the tan. So tan but instead of writing the theta symbol you're going to write 60° remember I said the theta this symbol right here it means the angle that is inside the triangle.

[00:19:48]All right. Equal our opposite. That's the X that we want to find.

[00:19:54]>> So X over >> adjacent. And adjacent is 15.

[00:20:02]>> 15 cm. But we can just write 15.

[00:20:06]All right. So our next move is to get the X by itself.

[00:20:10]So currently X is over 15.

[00:20:14]So since the 15 is dividing the x we have to multiply by 15. So carry the opposite operation of the division.

[00:20:24]So once you multiply those will cancel. And now I can switch this around. So 15 * tan 60= x. And I can change this to x = 15 * tan 60°.

[00:20:47]So as I was saying last week about the calculator going to keep these. Let's say that's 15 * 10 60.

[00:20:59]Let's jump over here the calculator screen.

[00:21:05]>> Yeah.

[00:21:07]And you have a scientific calculator at home, guys. Please use it.

[00:21:13]We plug plug the 15 in first.

[00:21:20]>> Plug the 15 in.

[00:21:23]All right. Person who are waiting on to be added. I'm going to add in a minute.

[00:21:27]So >> 15.

[00:21:29]>> So what number we going to use in what sign?

[00:21:34]Repeat.

[00:21:36]>> What number? We're going to use one sign.

[00:21:40]>> What number? We're going to use the one who >> we're going to use. We're going to do the 15 by what is the number >> 15?

[00:21:51]>> Yeah.

[00:21:56]>> Listen up. I'm saying 15 mip.

[00:22:08]>> So I'm on the calculator right now. So look on the calculator, right?

[00:22:16]>> All right. So I plug in the 50 >> and uh we said multiply, right? Let's see if I can zoom this screen a little bit more. All right, perfect. You see, look at these three words right here.

[00:22:36]So, I have sign >> my earphone.

[00:22:46]What's the question?

[00:22:50]>> What multip again?

[00:22:55]Ask again.

[00:22:57]>> What was 15 multiply by again?

[00:23:03]>> I'm going go right again. Look right here. So, let me show you.

[00:23:09]>> All right. 15. You see 15 in that green?

[00:23:14]>> Yeah.

[00:23:16]>> Okay. So, that I multiply by 60.

[00:23:24]Yes. You see that?

[00:23:27]>> Yeah.

[00:23:27]>> So, T A N 60°.

[00:23:36]>> I show that. All right.

[00:23:39]>> Yes.

[00:23:41]>> So, we just put the 15 in the calculator just now.

[00:23:46]>> I get 900.

[00:23:50]>> Hold on. Hold on.

[00:23:53]You see three right here. So >> yeah sign.

[00:24:00]>> Yeah.

[00:24:01]>> We go press 10 because what we had in the problem and then we're going to press 60 that came after the 10.

[00:24:15]Let me go again. So six zero now we close and we say equal.

[00:24:29]All right. So now I do it from my calculator.

[00:24:37]So All right. So the answer that we get is 15 equal sorry x = to let me clean this up= 26.

[00:25:08]All right. So this opposite side is 26 cm.

[00:25:14]Let me see who else needs to be added in the Google. Yes, >> 25.98 or 4.80.

[00:25:26]But >> exactly. But but we run it at 26.

[00:25:32]>> Okay.

[00:25:33]>> So, put it at 26. All right.

[00:25:36]Like the 15 and the um 15 * 60 * 15 * 10 15 * 10 60 >> what answer?

[00:25:57]>> Wait.

[00:25:59]So we're going to >> hear you call the answer while >> wait 26.

[00:26:08]>> How you tell me you get 26?

[00:26:11]How you get 26?

[00:26:14]First I I had the 15 I had the 15 times time 60 and I am getting I am getting um I am I am get I am getting 25.98 and and 40.80.

[00:26:40]>> All right pause this now. So that's what was on my calculator.

[00:26:45]So 25.9 8 0.

[00:26:53]But I rounded my number to 26.

[00:26:59]>> Yeah.

[00:27:00]>> You see how close 29.5 to 26?

[00:27:04]>> Yeah. So >> that's why I have it as 26.

[00:27:08]So I just kind of r it up a little bit.

[00:27:12]All right. All right. I'm going to jump to this screen right now.

[00:27:25]>> Yes. I I run it up to 26 YouTube kind of lazy man.

[00:27:34]Not even the free emojis them at all.

[00:27:38]Some not even know me on YouTube because ask a million one question already and not one person say Y or X not know how YouTube right now but continue.

[00:27:59]All right. So number one in this case, so find the missing side or angle round your answers to the nearest t.

[00:28:13]>> Yes, I audio check.

[00:28:16]>> I round it up and I get 25.98.

[00:28:23]>> Okay. Okay. All right. No problem.

[00:28:27]YouTube audio check for YouTube.

[00:28:30]you check on YouTube.

[00:28:34]I want to know if you guys hearing properly over YouTube.

[00:28:41]YouTube audio check. Give me some feedback.

[00:28:54]All right. So, all right. Thanks.

[00:29:00]We're looking on number one for this one.

[00:29:06]All right. So number one has a right triangle as >> So I got this. So 15 * tan 60° = 25.98.

[00:29:23]I'm running up gives you 26.

[00:29:28]All right. Yes. Perfect. That's what we did.

[00:29:32]Very good. So, let's move on to these other questions now.

[00:29:39]>> You think you think ready for these questions that we have?

[00:29:42]>> Yes.

[00:29:44]>> All right. So, do you know how to label this triangle?

[00:29:50]>> Wait.

[00:29:52]Number one. We're looking at A.

[00:29:55]Right. Number one. Yes.

[00:29:58]I don't.

[00:29:58]>> Do you know the name of the sides?

[00:30:01]>> Um, no.

[00:30:04]>> All right. So, we're going to label this one together right now.

[00:30:07]>> Okay.

[00:30:08]>> All right.

[00:30:10]So, before you can start the solution, >> you have to write the names of the sides first.

[00:30:21]You see this right angle symbol here, the square?

[00:30:27]Yes.

[00:30:28]>> You see once you identify that square and you draw that arrow where the arrow is pointing this side is called the hypotenuse.

[00:30:41]We just say hy >> learn I learned something like that at school.

[00:30:49]>> Exactly. So now it's going to reinforce your memory now.

[00:30:53]And then the angle that is given what angle do I have in the triangle?

[00:31:01]What angle is this?

[00:31:03]>> Um >> right here.

[00:31:11]>> What's what angle is this?

[00:31:17]Still don't know that the >> look on the screen. Look where look where the laser is pointing.

[00:31:26]>> What's this number?

[00:31:32]>> Come on, focus. What's this number?

[00:31:35]>> 35.

[00:31:38]>> That's exactly what may I ask you. So, wherever the angle is, you're going to draw that arrow. And then this is going to be our opposite side.

[00:31:50]And then we have our adjacent below.

[00:31:56]Sorry. So, this is our adjacent side below a DJ.

[00:32:03]All right. So next step we're going to choose the trig ratios or the trig ratio to use. So you were given the hypotenuse let's say 12 m hypotenuse and you're asked to find the opposite.

[00:32:23]So the trig ratio that has the hypotenuse and the opposite is going to be sin theta equal opposite.

[00:32:38]Guys, if we're not speaking, please turn off the the mic of a hypotenuse.

[00:32:47]All right. So once this is done, we simply just fill in the missing values.

[00:32:54]So sine, but instead of writing the angle theta, we're going to put the actual angle that is in the triangle.

[00:33:05]So this is going to be 35°.

[00:33:10]And then this is going to be equal to our opposite is x.

[00:33:17]That's what we want to find. And our hypotenuse is 12.

[00:33:24]All right. So, we want to get the x by itself.

[00:33:32]So, we have to multiply by 12 on both sides.

[00:33:39]All right. And then these 12s will cancel.

[00:33:42]So, it's kind of similar to the first one.

[00:33:46]And then we can switch this around to x = 12 * sin 35°.

[00:33:58]All right. So the first one was 15 * tan 60.

[00:34:05]Now this one is 12 * sin 35.

[00:34:13]So what is our answer for this one YouTube? What's our answer for this one?

[00:34:22]So x= 12 * sin 35. What is our length for the opposite?

[00:34:32]So take out your scientific calculator.

[00:34:42]>> Sir, it's >> 0.7.

[00:34:48]>> We're going to investigate one day.

[00:34:50]>> You said x what times? What time?

[00:34:56]X.

[00:34:58]>> Listen. Hold on. Hold on. Listen up. No pay attention. Listen here.

[00:35:05]>> Yeah.

[00:35:06]>> I come back. I say x * what times what times what times what? I'm never say x times anything.

[00:35:14]I said x is equal to 12 * sin 35.

[00:35:20]So that work with 12 * sin 35.

[00:35:27]Focus on that one.

[00:35:30]All right. So, let's go again. I heard somebody gave a a number earlier, a male. Please repeat the number.

[00:35:40]>> I heard something about 0 something.

[00:35:42]>> Sir, I said 0.72.

[00:35:49]>> All right, let's have a conversation now. Hold on. Hold on. Wait, wait a second.

[00:35:56]the person who said 0.

[00:35:58]Let's have a convo for a second.

[00:36:05]Xal hold on little miss. Hold on. Hold on.

[00:36:10]Hold on, man.

[00:36:13]Hold on there. Pause a little bit. We get everybody answer.

[00:36:20]All right. So, let's go again. So, the person who said 0.7 something, tell me what you typed in to get 0.7.

[00:36:32]I put 12 * 35.

[00:36:38]All right. So, this is the issue now.

[00:36:42]Sorry, you said you see this word right here? Hold on. Hold on. You see this word right here?

[00:36:50]S I N.

[00:36:53]You have to punch that in and then you put the 35.

[00:36:57]What type of calculator are you using?

[00:37:00]>> A scientific.

[00:37:04]>> Okay. So, you see when you plug in your 12, let me show you something.

[00:37:09]All right. Now, I help you get that.

[00:37:13]All right. So, when you plug in the 12, right?

[00:37:19]You seen this calculator on screen?

[00:37:24]>> Yes.

[00:37:26]>> Okay, good. So, punch in your 12 and press multiply.

[00:37:32]Do not press the 36 as yet.

[00:37:36]Look at these three words right here.

[00:37:40]Sign, cos, and tan.

[00:37:44]That's what we're using. So we have 12 * sign.

[00:37:51]We press the sign first and then we press the 35.

[00:37:58]>> You get it now.

[00:38:02]Yes. So once you see that once you see the word whether sign cost or tan >> we have to go up a top right up here.

[00:38:14]and press the button first and then you press the last number which is 35 >> and that's how you get your answer.

[00:38:25]So we have 6.88 and I only passed up. So we're going to round your answer now.

[00:38:35]All right. So we say okay and this says to the nearest nearest 10th. So if it's to the nearest 10th, what do you think this is going to become? So we had 6.886.

[00:38:54]If it's to the nearest 10th YouTube, what will it be? So what will it be approximated to? So 6.886 to the nearest 10th. What will be the new number?

[00:39:11]Huh?

[00:39:15]>> I don't understand.

[00:39:20]>> Nearest 10th, guys. What would be our new number?

[00:39:26]>> All right.

[00:39:28]So, that may have to go pull up something right now.

[00:39:34]All right, guys. Let's get this done.

[00:39:39]All right. Let's go.

[00:39:45]>> Boom. All right. So, on screen right here.

[00:39:51]So, I probably need to teach a lesson on >> Yay.

[00:39:56]>> place value.

[00:39:59]And place value. All right.

[00:40:02]>> Yes, sir.

[00:40:04]>> Cuz I realize now, say we're having a little bit of issue.

[00:40:11]understanding what the tens and sum mean. So I probably need to plan something on it. So let me plug in a new slide.

[00:40:24]All right.

[00:40:28]The 10th place guys is just persons who have the mics on. Please switch off your mic from please.

[00:40:38]Let me check who that is.

[00:40:39]>> I see the stuff that you're looking for now.

[00:40:45]>> Just mute your mic for a minute. Mute the mic now, please. All right. Thank you. All right. Let's go.

[00:40:55]So basically for the 10th place let's say we have a we have a number like 2 3.52 6.

[00:41:13]All right. the number that comes after the decimal point.

[00:41:19]This number right here, that's going to be 10th.

[00:41:25]All right. So, we're just focusing on this for now. So, if it say write your answers to the nearest 10th, >> sorry, all that going to be in the 10th place. means that the only one >> repeat.

[00:41:42]>> Oh, that's got in the 10th place >> the five tenth, not tenth.

[00:41:50]>> Oh, it's going to in the 10th place.

[00:41:52]10th place.

[00:41:55]>> It's supposed It's supposed to be in the 100th place.

[00:42:01]>> Check. Check your stats.

[00:42:05]Remember the one that comes immediately after the decimal point.

[00:42:12]>> That's 10th.

[00:42:16]>> All right? Because that is 1 / 10.

[00:42:19]That's 10th. And the two is going to be in the hundred's place.

[00:42:29]All right. And the six is going to be in what place?

[00:42:36]the thousand's place.

[00:42:39]>> All right. So, let's now go back to our screen. So, in this case, it means our answer is going to be 6.9 m cuz the answer says to the nearest 10th.

[00:43:02]All right.

[00:43:03]Hold on.

[00:43:06]Tries me check something.

[00:43:15]The person who I play game and I interrupt this the thing. Turn off your mic, please. Let me switch off your mic.

[00:43:22]They keep your mic muted nearly.

[00:43:29]All right, let's move on to the next question.

[00:43:37]All right, so we're looking at number two.

[00:43:41]So we were given so this is in cm.

[00:43:49]>> Oh sorry. So, so um 6,25.

[00:44:00]>> Okay, no problem.

[00:44:03]>> All right. So, we kind of move forward a little bit now. Look on your screen.

[00:44:08]That's what we focusing on now.

[00:44:11]>> Rules. Look at the digit right after the fact that in the the 100 place.

[00:44:18]>> Yeah, man. We do. So you never know. So we do that already.

[00:44:22]>> See we get the 6.9.

[00:44:26]Look on your screen now. That's what we doing on the screen.

[00:44:31]You have to follow a lesson because you play game in background and you missed the explanation.

[00:44:40]All right. So we're moving on to number two.

[00:44:45]YouTube space. What's going on for number two? Who got the answer for number two?

[00:44:54]So, first we need to label all the sides. So, this is going to be our hypotenuse.

[00:45:02]This is our opposite.

[00:45:04]This is our adjacent side.

[00:45:07]So, we first start out by labeling all the sides.

[00:45:14]And now we were given the length of the adjacent side and we are asked to find the opposite side.

[00:45:29]So the ratio that combines the opposite and the adjacent is the tan ratio.

[00:45:38]So tan theta equal opposite over adjacent.

[00:45:46]Let me put that a little higher.

[00:45:53]So tan theta equal opposite over adjacent.

[00:46:01]And as I said what from here we just fill out the rest of the information.

[00:46:08]guys. And remember that this angle that is in here in the triangle, we're going to replace this symbol with that angle in the triangle.

[00:46:23]So now we have 10.

[00:46:29]Let me adjust this.

[00:46:34]Hold on, guys.

[00:46:38]Let me adjust my pen tool.

[00:46:42]So 10, but instead of writing the data symbol, you're going to put 53.

[00:46:53]53 and it's kind of equal.

[00:47:02]The opposite side is x and the adjacent is 15.

[00:47:12]All right. So that's how this part looks. And then the person who told me the answer earlier, what's the answer for this one?

[00:47:25]15 on both sides.

[00:47:30]Sir after what? What?

[00:47:50]>> What's a question? Ask a question.

[00:47:57]>> Please go ahead with the question.

[00:48:02]All right. So, I want to plug this in your calculator.

[00:48:08]15 multiply by tan 52. Sorry, 53 >> 52 >> 15 * tan 53.

[00:48:25]Who's going to give us the answer for this one?

[00:48:29]15 * 10 53 equals to well 15 * 10 53.

[00:49:05]That's where we're at.

[00:49:16]All right. So our answer for that is going to be x= 19 9 05.

[00:49:31]But since they want the answer to the nearest 10th, it's going to be approximately 19.9 cm.

[00:49:46]All right. So, YouTube, wake up, man. Number three, how are we going to approach number three for calculating the missing angle?

[00:50:01]So, number one and two are pretty straightforward side calculation.

[00:50:08]But now we have been asked to find the missing angle in number three.

[00:50:19]>> How do you think we'll approach finding the missing angle for number three?

[00:50:26]>> YouTube Google Meet.

[00:50:30]How will we find the missing angle for number three?

[00:50:36]>> What's that?

[00:50:41]I don't understand number three.

[00:50:44]>> Right. So, we just reached a number three. So, we're going to work number three right now.

[00:50:49]What don't you understand about number three?

[00:50:55]Do you know how to label the sides?

[00:50:58]>> No, that's what I don't understand.

[00:51:00]>> Look on the look on the triangles at the top.

[00:51:06]What's the length of this side right here? Looking on the triangle at the top.

[00:51:13]>> X°.

[00:51:15]>> H >> X° >> this side. What's the length of this side?

[00:51:24]>> X°.

[00:51:27]>> No. No. X° is the angle that we're going to find right here.

[00:51:33]But we're looking on the this side right here.

[00:51:39]>> What's the name of the side?

[00:51:44]>> I just still don't know.

[00:51:46]>> So that side is our hypotenuse.

[00:51:51]And if the angle is here, this is going to be our opposite.

[00:51:59]And then the side below is our adjacent ADJ.

[00:52:06]>> What happened to >> what? Repeat.

[00:52:11]>> What happened to Ishmail?

[00:52:14]>> Focus on what we getting done right here.

[00:52:20]We're working mats right now. So focus on what we're doing.

[00:52:25]You get that?

[00:52:28]Okay. All right. So, let's go over here now.

[00:52:37]You see understand the time you ask me to explain.

[00:52:45]You're asking for people.

[00:52:49]So, we get the adjacent which is 20 and we get the opposite which is 12.

[00:52:56]We're going to use meter.

[00:53:00]So the trig ratio that we're going to use for this one is going to be an theta equal opposite over hypotenuse sorry adjacent over adjacent a dj guys it looks similar but the one different because angle we are find now. So it's going to be a little bit different at the last part.

[00:53:38]All right. So now we have 10 but previously we had a number to put right here which would have been the angle but now we have no number. We have x° So now we just put a x right here. So that's what we're trying to find.

[00:54:04]Equal our opposite is 12 and our adjacent is 20.

[00:54:14]So guys pay attention to this now. So we need to perform what is called the inverse of the trig ratio.

[00:54:24]So on the left side we have tan x but when we are finding angle we have to use the tan inverse operation.

[00:54:36]I'm going show you how to get that done.

[00:54:39]So this is now x equal and once you find an angle this is how you write the tan inverse tan with a -1 at the top right hand side and then you put the 12 over 20 in bracket right this already.

[00:55:07]All right. So, let me see. Tan inverse 1220.

[00:55:15]>> Let's go on the calculator now.

[00:55:19]>> Let's see what's there.

[00:55:22]>> Keep.

[00:55:26]All right. Let's go, guys. We get it.

[00:55:30]Calculator.

[00:55:33]All right. So we have so to get the inverse of tan.

[00:55:42]So normally we would just hold on let me keep the mics muted for the explanation.

[00:56:02]All right. So our problem is tan inverse 12 / 20. So to get the inverse of tan, we're going to press the shift button here at the top. So shift, you see a s command calculator, and then you press the key n.

[00:56:30]And if you notice, all right. So if we press only tan, you see tan by itself.

[00:56:43]But if we press shift and on some calculators it is called second function.

[00:56:53]then press the T.

[00:56:55]You're going to see a minus one that followed the word tan. So that's the inverse of tan or tan inverse.

[00:57:08]And then in the parentheses you're going to put 12 divided by 20 close equal.

[00:57:20]All right.

[00:57:22]So this is 30. Let's say 30.963.

[00:57:29]Let's finish this up.

[00:57:32]All right, let's get in.

[00:57:35]So our answer.

[00:57:38]So we had x= 30.9 63.

[00:57:49]So this is approximately we're going to use 40 since sorry we're going to use 31 not 40 so we're going to use 3 31 since the 9 is greater than five I rounded the 30 up to 31 any question YouTube Any question?

[00:58:23]Number two. So, what you got for number two, Ramsey? You say you didn't see that answer for number two? What did you get for number two answer?

[00:58:41]Violet Ramsey, what was your number two answer?

[00:58:47]And remember the calculator we nor round it to the nearest 10.

[00:59:03]My audio is poor.

[00:59:06]All right. So type in the chat what you got for your number two answer.

[00:59:16]Yeah. Thanks for the engagement.

[00:59:19]All right, number four.

[00:59:22]Whenever you're given all three sides.

[00:59:27]So in number four, just to label the sides, these are things. So number four, this side is we're going to be our hypotenuse.

[00:59:42]Then this is our opposite.

[00:59:46]And this is our adjacent right here. But if you notice audio check, guys. Audio check. Check.

[01:00:07]Audio check.

[01:00:09]All right.

[01:00:11]If you notice we are given all three sides.

[01:00:16]So in this case since all three sides, right? So you can use whichever ratio that you choose.

[01:00:37]So we're trying to find the angle X.

[01:00:42]So we have used sign and we use tan two times. So let's use cos for this one.

[01:00:53]All right. In order to use cost, we'll need the length of the adjacent and the hypotenuse.

[01:01:06]Since those are the two sides that are involved in the cost ratio.

[01:01:13]So cos theta is equal to adjacent a dj over hypotenuse.

[01:01:29]All right. and uh cos but instead of putting x sorry theta we're going to put the x cuz that's this x that we're trying to find me clean that up so I just put a x inside so that x here all right and then once we have this this is equal to adjacent of a hypotenuse So adjacent is 24, hypotenuse is 30.

[01:02:10]All right. And let's put meter on these.

[01:02:14]So now remember guys, if we are finding angles.

[01:02:22]All right. Uh I don't know what I did wrong but it was showing me.

[01:02:29]So if you're seeing a minus it's incorrect because you cannot have a negative length.

[01:02:38]If you have a negative length it means that the length is less than zero and no length is less than zero.

[01:02:51]All right. So 15 ult* by 1053 Ramsey.

[01:03:00]All right. Let's finish this up. So now that we have cos x = 24 over 30.

[01:03:09]We're going to keep the x by itself.

[01:03:12]So x will now be equal to cos inverse.

[01:03:22]So it's similar to the sin inverse and then we're going to have 24 over 30 in bracket.

[01:03:33]And now I'm going to head to the calculator and show you how we plug that in.

[01:03:39]All right.

[01:03:43]All right. Let's exit.

[01:03:46]So, so on our calculator guys, so remember whenever we deal with the inverse, we have to do the second function or the shift button right here. So, we press the shift button and we press cost.

[01:04:05]So, we're going to see cost with a negative one.

[01:04:09]All right, guys. This is the last one I'm finishing up. And then our numbers were 24 / 30.

[01:04:18]So 24 / 30 and we close the bracket.

[01:04:28]Can you plug number two in the calculator?

[01:04:34]All right. Equal.

[01:04:36]All right. So we have 36.86.

[01:04:40]86.

[01:04:42]So this is going to be 36 9 for our answer. I'm going plug number two in and then that will be our final solution for the day.

[01:04:59]All right.

[01:05:02]So what say your answer be again? X equ= 38 hold on 9 sorry 36.9 you guys heading out in a minute.

[01:05:27]All right so x equ= 36.9.

[01:05:33]All right. So number two 15 * 10 53.

[01:05:41]So number two 15 * 10 53 close.

[01:05:54]All right. So it's whenever I do it on the calculator that I have on online, I get a different answer. So I did it on my personal calculator.

[01:06:10]So 15 ult* by 10 53 and I got 19.9 zero and I rounded it to 19.9.

[01:06:26]So please check your calculators. It all depends upon on the calculator type. So please check the calculator. All right, guys. So, we're going to wrap things up right here.

[01:06:39]And don't ever use the iPhone calculator.

[01:06:44]That will give you a lot of messy answers.

[01:06:49]That's not accurate. All right. So, guys, we're going to wrap things up on this slide and we're going to step things up a little bit next class. But in terms of your homework, take a picture of this screen. Right? So >> what?

[01:07:11]>> Take a picture.

[01:07:13]>> Okay. Bye.

[01:07:15]>> Take a picture of the screen. That here.

[01:07:20]>> How would we do that?

[01:07:23]>> Take a picture of the screen.

[01:07:28]>> Okay.

[01:07:30]I did it.

[01:07:31]>> Just went through a barrage of examples earlier, so it's now time for you to try it on your own.

[01:07:38]>> All right, guys. So, we're going to wrap things up in 20 seconds.

[01:07:42]Take the picture and I'll see you guys on next week.

[01:07:47]>> Okay. Bye.

[01:07:50]>> All right.

[01:08:04]I put you to Y.

[01:08:25]I'm to exit this screen.

[01:08:31]All right, guys. I'll see you guys next week.

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