Even More Trig (I'm Sorry)

1) How would I find BC?

You can find BC using cosine rule.  You have 2 sides and the included angle so you can find the 3rd side.

So BC is $\sqrt{19}$.

Then, by the law of sines, sin BCP is $\frac{\sqrt3}{\sqrt{19}}$.

What now?

If

 $sin\angle{PCB}=\frac{\sqrt3}{\sqrt{19}}\\ then\\ \angle{PCB}=sin^{-1}\frac{\sqrt3}{\sqrt{19}}\\ \angle{PCB}\approx 23.413 ^{\circ}$

Now, check you know how I did that on a calculator and then move onto step 3

sorry it has not displayed properly, I will see if I can fix it.    It is fixed I hope.

Thanks for the help! I figured out the answer! :)