Triangle ABC is given where m(angle)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.

Answer 1

This is referred to as the "ambigious case"
From the given:
9/AC = sin33
AC = 9/sin33 = appr 16.5

now by the sine law sin(angle ABC) /16.5 = sin33/15
sin(angle ABC) = .6
angle ABC = 36.9° or angle ABC = 180-36.9 = 143.1°

So, two angles
both triangles can be drawn

Answer 2

Thank you Reiny!

Answer 3

Is Reiny correct? Please someone tell me.