Exercise 38 Page 656

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 T = Length of leg opposite to∠ T/Length of hypotenuse In our triangle, we have that the length of the opposite leg to ∠ T and the hypotenuse are 25 and 30.

sin T = opposite/hypotenuse

SubstituteII

opposite= 25, hypotenuse= 30

sin T = 25/30

ReduceFrac

a/b=.a /5./.b /5.

sin T = 5/6

The sine of the angle is 56. Now, to isolate m∠ T we will use the inverse function of sin. sin T=5/6 ⇔ m∠ T=sin ^(- 1)5/6 Let's use a calculator to find the value of sin ^(- 1) 56. 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 56, and press ENTER.

The angle is about 56.4^(∘).