In Exercises 65–68, ABC is a right triangle with the right ang...

Question

In Exercises 65–68, ABC is a right triangle with the right angle at C. The sides opposite angles A, B, and C are a, b, and c, respectively.

a. Express sin A in terms of a and c.

b. Express sin A in terms of b and c.

Accepted Answer

Welcome back, everyone. A right triangle PQR has a right angle at R. The sides PQ and R are opposite the angles PQ and R respectively. Express cosine of Q in terms of P and R were given for answer choices A says PR, B 1/2 PR, C P divided by R, and DR divided by P. So let's draw a right triangle. Specifically, we know that we have a right angle at R and we're going to add the remaining Q and P. Wherever we want, right? Because it's not specified. So now we want to express cosine of Q, and we know that we have three sides, PQ and R opposite to PQ and R respectively. So first of all, let's begin with q. We're going to add lowercase q as a side opposite to that angle, lowercase r opposite the angle r, and lowercase p opposite the angle p. And now we want to write cosine of q. Let's recall that cosine, according to Soatoa, is the adjacent side divided by hypotens, and our adjacent side is essentially P. So that's our adjacent and our hypotenuse in this context is R. That's how we're hypotenuse. So now, cosine of Q is the ratio between adjacent and hypotenuse. We can say adjacent side. Divided by Hypoten. And in this problem our adjacent side is P. Our hypotenuse is R. Therefore, we have arrived at the answer cosine of Q equals p divided by r, which corresponds to the answer choice C. Thank you for watching.

In Exercises 65–68, ABC is a right triangle with the right angle at C. The sides opposite angles A, B, and C are a, b, and c, respectively.a. Express sin A in terms of a and c.b. Express sin A in terms of b and c.

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In Exercises 65–68, ABC is a right triangle with the right angle at C. The sides opposite angles A, B, and C are a, b, and c, respectively.

a. Express sin A in terms of a and c.
b. Express sin A in terms of b and c.