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.