Question from Carla, a student:

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

Remember that any arc on a circle is subtended by an angle from the circumference which is half of the measure of the angle from the circle's center, then you can quickly draw the corresponding central angle:

Notice that the two blue lines are the same length, so use your knowledge of the ratios of a 30-60-90 triangle to determine the length of the blue line in the right triangle inside.

Cheers,
Steve La Rocque.