Exercise 38 Page 796

We are given the length of one leg and the measure of an acute angle of a right triangle. We will find values of x and y one at a time.

Value of x

x is a length of the hypotenuse.

Note that the given side is opposite to the given angle, and the side we want to find is the hypotenuse of the triangle. Therefore, we will use the sine ratio. sin θ = opposite/hypotenuse In our triangle, we have that θ = 50^(∘) and the length of the opposite side is 71.8. We want to find the length of the hypotenuse.

Value of y

y is a length of the side adjacent to the given angle.

As we can see, the given side is opposite to the given angle, and the side we want to find is adjacent to the given angle. This means that we will use the tangent ratio. tan θ = opposite/adjacent Similar as before, we have that θ = 50^(∘) and the length of the opposite side is 71.8. Let's find the length of the leg adjacent to the angle.