Triangle ABC is given where angle A=64 degrees, a=16 in., and the height, h, is 15.3 in. How many distinct triangles can be made with the given measurements? Please explain your answer to your best ability

Answer 1

Let the base of the triangle be side AB, with the altitude h from C meeting AB at point D.

Since side a is greater than h, there are two triangles possible, one with B between A and D, and one with D between A and B.

Note that if a > h/sinA then there is only one triangle.