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:
[tex]\begin{gathered} \frac{\sin R}{\cos R}=\frac{\frac{ST}{RS}}{\frac{RT}{RS}}=\frac{ST}{RT}=\tan R \\ \tan (29)=\frac{ST}{RT}=\frac{6.7}{RT} \\ RT=\frac{6.7}{\tan (29)}=\frac{6.7}{0.554}\approx12 \end{gathered}[/tex]The length of TR is 12 feet.
