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Math Help - Largest angle of a triangle

  1. #1
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    Largest angle of a triangle

    Triangle ABC has side lengths a,b and c. If these lengths satisfy a^2=a+2b+2c and 3=a+2b2c, what is the measure (in degrees) of the largest angle?
    I applied a bit of cosine rule and sine rule, but all it gave was nasty equations in angles of the triangle.
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  2. #2
    Junior Member Bradyns's Avatar
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    Re: Largest angle of a triangle

    If it helps... the largest angle is opposite the largest side.
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  3. #3
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    Re: Largest angle of a triangle

    There must be a unique triplet of numbers a b c that satisfies those two equations. By trial and error, I'm pretty sure I found it.

    a=5 b=3 c=7

    From that it's easy to find the measure of the largest angle using the law of cosines.

    So far I can't solve those equations systematically though.
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  4. #4
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    Re: Largest angle of a triangle

    Adding the two equations you get a^2 - 3 = 2a +4b. At a = 3, b becomes zero. So a must be greater than 3.
    At a = 4 , b = 5/4 . If you put this value in the first equation, you get negative c which is not possible.
    At a = 5, b= 3 and c = 7.
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