Q:

What is measure of angle R?Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.What is measure of angle P?Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.Both questions use the same pic

Accepted Solution

A:
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 :- [tex] sin(\theta)=\frac{Opposite}{Hypotenuse} [/tex] For angle R, opposite side would be PQ. [tex] 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 [/tex] For angle P, opposite side would be QR. [tex] 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 [/tex]Hence, R = 28.07 degrees and P = 61.93 degrees.