Triangle abc is given where m(angle sign)a=33 degrees, a=15 in, and the height, h, is 9 in. how many distinct triangles can be made with the given measurements? explain your answer.

You could have an infinite amount of triangles with these measurements.

Unless, you are missing something in the problem, there is not enough information that would narrow it down to a single triangle. Angle A is fixed and the height is fixed. However, Angle B and C could be anything as long as they formed a triangle and had side a of 15 in between them.