How to use the cosine rule to find a side in trigonometry.

We are going to use the cosine rule. Let me give you a hint so that you know you are going to use it. the cosine rule, and not the sine rule, is what you should use; notice that we have something Like a V here, you have a V there, there is an angle given, and you are providing the sides as well. So whenever you see this sign, you'll have a V, like a V, right? Yeah, you have a V, you have a V. The angle is given, and the two sides enclosing the angle are given as well. Go ahead and use your cosine rule to find x, even if it's for the sine rule. Okay, let's leave that one aside. Let's just focus on what we have; this is what is showing me. Now let's go ahead and solve the equation. Now one thing that students find hard is how to Memorize the cosine rule—it's actually very easy. Now let me tell you how I know mine. You know that. When you have your triangle, for example, this is what we have here: we have a, we have b, we have c. Okay, know that the side facing you, the capital A, is your small a, the side facing you. Capital B is your small b; the side facing your capital C is your small c. Okay, that is the first. The one thing you need to know now is what you need to know again—the only thing now is for you to know. how to write your um what is it called your formula notice that you are looking for x that Is the small A because that's the side facing our A, so what do we do then? This is it, your small. a squared okay is going to be equal to now you are what you are going to make use of just small b and c because you're looking for small a; just see what I'm trying to say— you write your b squared plus c squared, that's because you're looking for side a—just make use of your b and c minus 2bc, notice that I'm still making use of my bc because it's not when you write cos because You are going to use the cosine root; it's not when you write cos that you are going to bring it. In your A, your capital A, you see what I did? Very easy, because I'm looking for side A, I'll write my a squared is going to be equal to everything I'm going to use here, mostly the b and The C, the small b, and the small c—the only place my A is going to come in again is what my capital. So it's going to be b squared plus c squared minus 2bc times cosine a. Very easy now we go ahead and Bring out our parameters now. When you look at this, you are going to notice something—you are You're going to know that your capital A is what 38 degrees now, your small a is what we are looking for. For this one, your small b is the side facing your capital B, which is 15. Your small c is the side facing your capital C, which is 19, so we go ahead and substitute this thing that we got into this particular equation, so let's go ahead and do that. So our a squared, which is what we We are going to have 15 squared plus our c is what 19, 19 squared minus 2 times our b is what our b It's 15 times our C, which is 19, because our capital A is 38, so all you need to do there is just substitute. Very, very easy now we go ahead and solve this. Our a squared is equal to 15 squared, which gives us 225, right? 225 plus 19 squared. We get 19 squared, which gives us 361. So we write 361. Minus 2 times 15 is 30. 30 times 19 is going to give us 570. So we have 570. cos 38 degrees, okay, so a squared is going to be 225 plus 361, which gives us 做完 Now 570 times cos 38. If we press that, we're going to get 570 times cos 38. We're going to get four four nine point one six six one four four nine point one six six one I don't want to approximately okay, so my a squared is going to be equal to, so we're going to have 586 minus four forty-nine, so we are going to have one thirty-six point eight three three okay let's stop at eight three four okay now our a is going to be what square root of one three six point eight three four and this is going to give us square root of one three six 0.834 will give us 11.698, which we can write as okay in centimeters, right? Yes, in centimeters, which we can round off to 11.7 centimeters to one decimal place. And this becomes our solution. Thank you so much for watching, and I wish to see you next time. Goodbye