MATHS TRIGONOMETRY

Hinzugefügt: 2026-06-03

[00:00:00]Hello, dear learners. How are you today?

[00:00:04]I'm very much sure that you are doing well.

[00:00:08]This is mathematics and with me is a question that I want you to pay attention to as I'll be solving.

[00:00:18]Please, I want you to watch the video up to the end because I've got good news for you.

[00:00:25]Okay?

[00:00:26]Let's look at the question.

[00:00:29]The diagram below shows a right-angled triangle P Q R.

[00:00:38]So, what you're seeing here is a right-angled triangle.

[00:00:43]How do you tell that this is a right-angled triangle?

[00:00:47]Have you seen this square here? It indicates that it is a right-angled triangle.

[00:00:56]Further, it says, "Given that PQ the length PQ from P to Q is equal to 15 cm and cos X degrees is equal to this ratio 2/3."

[00:01:17]Now, the question says, "Calculate the length of QR."

[00:01:23]QR.

[00:01:25]We want to know the length of this.

[00:01:28]We are told that this length is 15 cm.

[00:01:33]And the type of triangle we are dealing with is a right-angled triangle.

[00:01:38]Remember, we have different types of triangles, right? The scalene triangle, isosceles triangle, and others.

[00:01:47]Now, how do you calculate this length?

[00:01:52]This topic, ladies and gentlemen, is trigonometry.

[00:02:00]Upon realizing that this is trigonometry, you will be able to recall some of the things that you've learned.

[00:02:10]Like calculating length or angles in a right-angled triangle, we only use one the Pythagoras theorem.

[00:02:37]The other one that we can use is the SOH CAH TOA.

[00:02:50]So, whenever you are Please get me very well there.

[00:02:54]These two only works when you are dealing with this type of a triangle.

[00:03:03]Not any other triangle, but only a right-angled triangle.

[00:03:12]The Pythagoras theorem and SOH CAH TOA.

[00:03:18]Pythagoras theorem, we only use this one to calculate length, like the way they've asked here.

[00:03:26]But bear in mind that you can only use this one when you are given two sides.

[00:03:32]15 cm, if we are given another side here, then they are asking us to find this.

[00:03:39]We'll be able to use Pythagoras theorem.

[00:03:42]But in this case, look at it. We are only given one side, 15 cm. We don't know this length. We don't know this length.

[00:03:52]Therefore, we cannot use Pythagoras' theorem.

[00:03:57]That means the only option that has remained is SOH CAH TOA.

[00:04:02]Now, how do we use this SOH CAH TOA?

[00:04:05]On a right-angled triangle.

[00:04:08]This S We have three ratios here.

[00:04:13]Okay?

[00:04:14]Sine, cosine, and tangent or tan.

[00:04:20]These are the three ratios.

[00:04:22]Now, you have to identify which ratio must be used here.

[00:04:30]How do we identify?

[00:04:33]First, we have to name the three sides. They've got names.

[00:04:38]Look at this.

[00:04:40]Angle is at this point.

[00:04:43]Angle X.

[00:04:44]If the angle is here, meaning this becomes your opposite. Are you seeing O?

[00:04:52]O, that indicates opposite.

[00:04:54]So, if the angle is here, this is your opposite. If the angle was here, this could have been our opposite.

[00:05:03]So, we have named this one, opposite.

[00:05:06]What next?

[00:05:08]The longest side is always your H, hypotenuse.

[00:05:16]The longest side or the side that is always opposite to the 90° angle. This one is always in the hypotenuse. Meaning the remaining side is your adjacent. These are the three we are seeing here.

[00:05:32]Opposite, hypotenuse, adjacent, hypotenuse, opposite, adjacent. Are you seeing that?

[00:05:39]Now, we need to pick which ratio must be used here for us to find Remember, we want to find QR, meaning this length.

[00:05:49]In short, we want to find the adjacent.

[00:05:52]So, if we are looking for the adjacent and we've been given hypotenuse, we are not going to use O.

[00:06:02]We don't want this one.

[00:06:04]We only be able to concentrate on the one that we are looking for and the one that we have been given.

[00:06:11]So, it is AH.

[00:06:15]I see that.

[00:06:17]It is AH. These are the ones that we are going to use. Now, let's identify the ratio that has got AH.

[00:06:25]It is this one here.

[00:06:29]I see the way I'm identifying. I'm not going to use this one because I don't know opposite. I've not been given opposite. And this one has got opposite.

[00:06:37]So, I can't use these two. So, it is this.

[00:06:40]The moment you identify the ratio, you are going to write it in this way.

[00:06:45]cos I see that.

[00:06:49]cos angle, in this case it is cos X.

[00:06:55]I see that.

[00:06:56]degrees will be equal to cos is adjacent. We come here. What is our adjacent? It is the one that they are asking us to find, QR.

[00:07:12]So, it will be QR over hypotenuse, which is this 15.

[00:07:20]All right, 15.

[00:07:23]Are you seeing the substitution there?

[00:07:27]This is the substitution. Now, we are told that the ratio cos X degrees is equal to 2 over 3. That is the ratio.

[00:07:37]This one here now is equal to 2 over 3.

[00:07:40]So, where there is this, I substitute 2 over 3.

[00:07:44]That is equal to QR over 15. We want QR.

[00:07:53]Cross multiply.

[00:07:56]Three times QR will give us three QR is equal to two times 15 will give us 30.

[00:08:06]Divide by three, divide by three. So, finally, QR will be equal to how many threes are in 30? 10.

[00:08:18]So, this length here is 10 cm.

[00:08:24]I hope you understood.

[00:08:26]Is this concept clear to you?

[00:08:30]Please, I want you to watch the video again so that you understand everything that I've said here.

[00:08:38]I want to tell you that we are providing online lessons.

[00:08:45]Wherever you are, you just be able to learn without any contact, without you coming for physical classes. Everything will be done just there in your home.

[00:09:02]So, we have from grade five to seven. We also have form one, form two, grade 10, 11, 12, and the bigger ones, the GCE.

[00:09:22]Few months, few weeks should I say, have remained for GCE. Join now. I'm just giving you five days especially for this to join.

[00:09:34]If you're not going to join the U this.

[00:09:36]I'm not going to accept.

[00:09:39]Okay? So, we have English language, mathematics, biology, and science.

[00:09:48]Those are the major ones that are currently going on. Together with those who are doing additional mathematics, contact me now.

[00:10:07]You see that?

[00:10:08]If you're outside the country, you just add this 26 here.

[00:10:13]This is the number that you should contact me. You will be able to receive everything. Not only videos, exercise, pamphlets, reliable pamphlets.

[00:10:23]The test will also be given. It's a full capacity.

[00:10:28]They are pre-recorded videos. You can download them, watch them at your own free time, at any time.

[00:10:36]Exercise will be given. You submit just like that.

[00:10:41]Is that not what you want?

[00:10:43]I see that. So, I'll be able to give you you just inbox me, you call me, be able to give you full details on the payments, and you start immediately at any time.

[00:10:55]Don't waste much time. You have already Your friends have already started. I must make mention. I must tell you. So, they are learning.

[00:11:05]Immediately you watch this video, contact me, make payment, and start learning.

[00:11:12]Is that clear? For the grade sevens, six, five, it is all the subjects.

[00:11:19]Form one, form two, mathematics, English, bio biology, physics, chemistry, ICT.

[00:11:28]Please, don't forget to share the video to others.

[00:11:34]Follow me on TikTok and subscribe to my YouTube channel.

[00:11:38]Introductory Nadi. Thank you very much for trusting my work. Thank you very much for watching this video. Bye-bye.