How Many Different Triangles?

Sam is designing a triangular piece for a metal sculpture. He tellsMartha that two of the sides of the piece are 40 inches and 15 inches,and the angle opposite the 40-inch side measures 120°. Martha decidesto sketch the piece that Sam described. How many different triangles

can she sketch that match Sam’s description?

I understand that this is a law of cosines problem. I can find the missing side. However, how do I find the number of different triangles for such a triangle?