Question

What is measure of angle R?

Answer 1

Given is a Right triangle PQR with angle Q = 90 degrees.

Given are sides PQ = 8 cm, QR = 15 cm, PR = 17 cm.

Side PR is the hypotenuse.

We can use formula for "sin" given as follows :-

$sin(\theta)=\frac{Opposite}{Hypotenuse}$

For angle R, opposite side would be PQ.

$sin(R)=\frac{PQ}{PR} \\\\ sin(R)=\frac{8}{17} \\\\ sin(R)=0.470588235 \\\\ R=sin^{-1}(0.470588235) \\\\ R = 28.07248694 \;\;degrees \approx 28.07 \;degrees$

For angle P, opposite side would be QR.

$sin(P)=\frac{QR}{PR} \\\\ sin(P)=\frac{15}{17} \\\\ sin(P)=0.882352941 \\\\ P=sin^{-1}(0.882352941) \\\\ P = 61.92751306 \;\;degrees \approx 61.93 \;degrees$

Hence, R = 28.07 degrees and P = 61.93 degrees.