MATHS TRIGONOMETRY

追加: 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?

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