Exercise 16 Page 536

We are given the length of one leg and a hypotenuse of a right triangle, and want to find the measure of one of its acute angles.

Note that we are given the opposite side to the unknown angle and the hypotenuse. Therefore, to find its measure we will use the sine ratio. sin x = Length of leg opposite tox/Length of hypotenuse In our triangle, we have that the length of the opposite to x and hypotenuse are 12 and 22.

sin x = Opposite/Hypotenuse

SubstituteII

Opposite= 12, Hypotenuse= 22

sin x = 12/22

ReduceFrac

a/b=.a /2./.b /2.

sin x = 6/11

The sine of the angle is 611. Now, to isolate x we will use the inverse function of sin. sin x=6/11 ⇔ x=sin ^(- 1)6/11 Let's use a calculator to find the value of sin ^(- 1) 611. First, we will set our calculator into degree mode. To do so, push MODE, select Degree instead of Radian in the third row, and push ENTER. Next, we push 2ND followed by SIN, introduce the value 611, and press ENTER.

The value of x is about 33.1.