I am (slowly) working my way through "Teach Yourself: Understand Trigonometry" by Hugh Neill and already I've encountered a problem which has me stumped.

Exercise 2.3, problem 4:

PQRS is a rectangle. A semicircle drawn with PQ as diameter cuts RS at A and B. The length PQ is 10cm, and angle BQP is 30 degrees. Calculate the length PS.

As I'm still working my way through some basic material from geometry I'm sure I'm missing something really obvious. I've sketched what I think the set-up should be:

and I'm thinking solving it has something to do with the geometry of a trapezoid but I'm just hitting walls! I should also point out that it's only in the second chapter of the book and so the problem must be solved using only basic rules of sine, cosine and tangent (SOHCAHTOA).

Help?!?