Question

In ARST, the measure of ZT=90°, the measure of ZS=21°, and ST = 7.7 feet. Find the length of TR to the nearest tenth of a foot. S 21° 7.7 T х E

Answer 1

In ΔRST, the measure of ∠T=90°, the measure of ∠R=29°, and ST = 6.7 feet. Find the length of TR to the nearest tenth of a foot.

We will draw the rectangle triangle:

We can use the trigonometry property where the sine of an angle (∠R) is equal to the ratio between the opposite side (ST) and the hypotenuse (RS).

Also, the cosine of ∠R is equal to the ratio between the adyacent side (RT) and the hypotenuse (RS).

We can express this as:

`\begin{gathered} (\sin R)/(\cos R)=((ST)/(RS))/((RT)/(RS))=(ST)/(RT)=\tan R \\ \tan (29)=(ST)/(RT)=(6.7)/(RT) \\ RT=(6.7)/(\tan (29))=(6.7)/(0.554)\approx12 \end{gathered}`

The length of TR is 12 feet.