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Math Help - Quick Question: Solving Triangle

  1. #1
    JoH
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    Quick Question: Solving Triangle

    Hello,

    The question is solve the triangle where a = 22.24 cm, b = 9.74 cm, A = 33.3 degrees.

    I understand that it is an SSA triangle so I use a/sinA = b/sinB. I plug that in being 22.24/sin33.3 = 9.74/sinB. I then solve for sinB.
    -----> sinB = 9.74sin33.3/22.24 - I then get sinB = .2404. Now here is my problem. It says there are two angles that are less than 180 degrees that have the sine = .2404.
    How do I find these two angles? The answer states that the two angles are 13.9 degrees and 166.1 degrees. How would one go about finding them?

    I understand the rest of the problem, besides that part (finding the two angles).

    Thanks for the help
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  2. #2
    MHF Contributor
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    Re: Quick Question: Solving Triangle

    the two angles B that are such that sin(B) = (b/a) sin(A), using the numbers for a,b,A are

    13.91 and 166.09 degrees.

    The interior angles of a triangle sum to 180 degrees. You are given one of it's angles is 33.3 degrees.

    166.09 + 33.3 = 199.39 > 180

    so clearly the correct angle is 13.91 degrees.
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