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Math Help - How Many Different Triangles?

  1. #1
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    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 120į. Martha decidesto sketch the piece that Sam described. How many different triangles
    can she sketch that match Samís 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?
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  2. #2
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    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 120į.
    Martha decides to sketch the piece that Sam described.
    How many different triangles can she sketch that match Samís 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.]

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  3. #3
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    ok

    Quote Originally Posted by Soroban View Post
    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?

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