There are two noncongruent triangles that have a 9-inch side, a 10-inch side, and that enclose 36 square inches of area. Find the length of the third side in each of these triangles.

Answer 1

If the angle θ between the sides is acute, then

(9 sinθ)(10)/2 = 36
θ = 53.13°
and the third side s comes from
s^2 = 9^2+10^2-180cos53.13°
s = √73

The angle might be obtuse. A little thought should show how to handle that case.

Answer 2

iki