Given: triangle PQD, PD = 12cm, angle Q = 30 degrees, angle D = 90 degrees. Find PQ.

we are given a triangle, based on the condition that the angle D is 90 degrees, we can conclude that the triangle is rectangular.
we are given a leg PD = 12 cm
find the hypotenuse PQ
because the leg, lying opposite an angle of 30 degrees, is equal to half of the hypotenuse
we can easily find the side PQ (because the triangle is right-angled and the angle Q is 30 degrees)
PQ = 12 times 2 = 24 cm
Answer: PQ = 24 cm