Question

State whether the given measurements determine zero, one, or two triangles.

C = 30°, a = 32, c = 16

Answer 1

One

Explanation:

A = 90°

By the law of sines, angle A must be 90 degrees. That makes side a the hypotenuse of a 30-60-90 triangle. There is only one triangle. The third side is 16√3, and the third angle 60°.

Answer 2

I bet you're doing the Law of Sines right now. If you use the law of sines you find out that angle A is a 90 degree angle. There is only one triangle you can make with these measurements because if you have one angle of 30 and another of 90, the 3rd angle has to be a 60 degree angle. So it is a special right triangle, 30-60-90