Triangle ABC is given where the measure of angle a is 33°, a=15 in., and the height, h, is 9 in. How many triangles can be made with the given measurements? Explain your answer.

Answer 1

Draw the base AX of the triangle, with AX nice and long.
Draw angle A, making the other side nice and long.
Mark C and drop an altitude to D on AB. Label the height CD=9

Now draw an arc of radius 15 centered at C, and you will see that it intersects AX at two points. Either of those could be labeled B.

Note that 9/AC = sin33°. So, AC = 16.52

Note that if side a had been longer than that, it would have been so long that one of the intersections on AX would have been outside the angle, so there would only be one triangle.