Question

What is the measurement of angle p? Round your answer to the nearest degree.

A. 29°

B.42°

C.65°

D.78°

Answer 1

You can use the law sines, which states that in a triangle the ratio between one side length and the sine of the opposite angle is constant.

So, we have

`(PR)/(\sin(Q))=(QR)/(\sin(P))=(PQ)/(\sin(R))`

In particular, we can use

`(PR)/(\sin(Q))=(QR)/(\sin(P))`

to write

`(68)/(\sin(73))=(47.6)/(\sin(P)) \iff \sin(P) = (47.6\sin(73))/(68)\approx 0.66`

Which means

`P\approx \arcsin(0.66)\approx 42`