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

Question

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

Steve · Accepted Answer

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.