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Math Help - law of cosines

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    law of cosines

    consider a triangle with known sides a=0.5, b=2, and c=0.5, how could i use law of cosine to find an unknown angle between sides a and b, i tried to use law of cosine it gave me cos(ab)=2, which is impossible

    please help
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    Quote Originally Posted by aukj View Post
    consider a triangle with known sides a=0.5, b=2, and c=0.5, how could i use law of cosine to find an unknown angle between sides a and b, i tried to use law of cosine it gave me cos(ab)=2, which is impossible

    please help
    This is an impossible triangle. It does not conform to the triangle inequality!
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    Quote Originally Posted by aukj View Post
    consider a triangle with known sides a=0.5, b=2, and c=0.5, how could i use law of cosine to find an unknown angle between sides a and b, i tried to use law of cosine it gave me cos(ab)=2, which is impossible

    please help
    The Cosine Rule states that

    c^2 = a^2 + b^2 - 2ab\cos{C}.


    In your case, a = \frac{1}{2}, b = 2, c = \frac{1}{2}.

    So by the Cosine Rule...

    \left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)^2 + 2^2 - 2\left(\frac{1}{2}\right)(2)\cos{C}

    \frac{1}{4} = \frac{1}{4} + 4 - 2\cos{C}

    0 = 4 - 2\cos{C}

    2\cos{C} = 4

    \cos{C} = 2.


    You are correct, this equation can not be solved. That means that this triangle does not exist... This is easily verified by the triangle inequality...
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    thanks
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