Exercise 13 Page 655

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 adjacent side to the unknown angle and the hypotenuse. Therefore, to find its measure we will use the cosine ratio. cos Z = Length of leg adjacent to∠ Z/Length of hypotenuse In our triangle, we have that the length of the leg adjacent to ∠ Z and the hypotenuse are 10 and 14.

cos Z = adjacent/hypotenuse

SubstituteII

adjacent= 10, hypotenuse= 14

cos Z = 10/14

ReduceFrac

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

cos Z = 5/7

The cosine of the angle is 57. Now, to isolate m∠ Z we will use the inverse function of cos. cos Z=5/7 ⇔ m∠ Z=cos ^(- 1)5/7 Let's use a calculator to find the value of cos ^(- 1) 57. 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 COS, introduce the value 57, and press ENTER.

The angle is about 44.4^(∘).