# Thread: How Many Different Triangles?

1. ## 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?

2. Hello, magentarita!

Sam is designing a triangular piece for a metal sculpture.
He tells Martha 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 decides to sketch the piece that Sam described.
How many different triangles can she sketch that match Sam’s description?
Did you try to make a sketch yourself?

You'll find that, with an obtuse angle, there is only ONE triangle possible.

[By the way, we need the Law of Sines to solve this triangle.]

3. ## ok

Originally Posted by Soroban
Hello, magentarita!

Did you try to make a sketch yourself?

You'll find that, with an obtuse angle, there is only ONE triangle possible.

[By the way, we need the Law of Sines to solve this triangle.]
I can use the Law of Sines to solve.

You said:

"You'll find that, with an obtuse angle, there is only ONE triangle possible."

Why is that the case?