Exercise 41 Page 656

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

Note that we are given the opposite and the adjacent sides to the unknown angle. Therefore, to find its measure we will use the tangent ratio. tan T = Length of leg opposite to∠ T/Length of leg adjacent to∠ T In our triangle, we have that the length of the opposite and adjacent legs to ∠ T are 4sqrt(3) and 10sqrt(3).

tan T = opposite/adjacent

SubstituteII

opposite= 4sqrt(3), adjacent= 10sqrt(3)

tan T = 4sqrt(3)/10sqrt(3)

ReduceFrac

a/b=.a /sqrt(3)./.b /sqrt(3).

tan T = 4/10

ReduceFrac

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

tan T = 2/5

The tangent of the angle is 25. Now, to isolate m∠ T we will use the inverse function of tan. tan T=2/5 ⇔ m∠ T=tan ^(- 1)2/5 Let's use a calculator to find the value of tan ^(- 1) 25. 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 TAN, introduce the value 25, and press ENTER.

The angle is about 21.8^(∘).