Roman C. answered • 04/02/16

Masters of Education Graduate with Mathematics Expertise

Another way of looking at it is this.

In triangle ABC, let sides a and b be given and also angle A.

Case 1: a < b sin A.

No possible triangles.

Case 2: a > b sin A.

Two triangles possible. They differ by mirroring side a about the altitude dropped from vertex C. Hence at least one of the solutions will be an obtuse triangle.

Case 3: a = b sin A.

Unique solution. This case corresponds to the HL theorem for right triangles.

Billy J.

04/03/16