Question

In ΔRST, the measure of ∠T=90°, the measure of ∠S=66°, and ST = 2.2 feet. Find the length of TR to the nearest tenth of a foot..

Answer 1

`TR=4.9\ ft`

Explanation:

see the attached figure to better understand the problem

we know that

In the right triangle TRS

The tangent of angle ∠S is equal to divide the opposite side to angle ∠S (TR) by the adjacent side to angle ∠S (TS)

so

`tan(S)=(TR)/(TS)`

we have

`\angle S=66^o\\TS=2.2\ ft`

substitute

`tan(66^o)=(TR)/(2.2)`

solve for TR

`TR=(2.2)tan(66^o)`

`TR=4.9\ ft`