Question

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

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

$\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}=\dfrac{PQ}{\sin(R)}$

In particular, we can use

$\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}$

to write

$\dfrac{68}{\sin(73)}=\dfrac{47.6}{\sin(P)} \iff \sin(P) = \dfrac{47.6\sin(73)}{68}\approx 0.66$

Which means

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