Trigonometery for math whiz!?

Question

Find PB.

Triangle APB Angle ABP is right.

C is a point on AB one unit away from A.

Angle PCB is 35

angle PAB is 30
THANKS!

Answer 1

I drew the picture and worked with triangle ACP first.
Angle ACP =145
angle APC =5
Using the law of sines sinA/a = Sin B/b
5/1 = 30/ x
x = 6, PC=6
Using law of sines to find PA
5/1 = 145/x PA =29
Since triangle ABP is a 30-60-90 triangle, You know the hypoteneuse is twice the short leg.
so BP is 14.5
It checks out.