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Math Help - Angle in a triangle

  1. #1
    Senior Member Mukilab's Avatar
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    Angle in a triangle

    The length of the sides of a triangle are 4.2, 5.3 and 7.6.

    Calculate the size of the largest angle of the triangle to 1 dp.

    How would I know this without calculating the area using 1/2 a b sin(c)????
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  2. #2
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    Quote Originally Posted by Mukilab View Post
    The length of the sides of a triangle are 4.2, 5.3 and 7.6.

    Calculate the size of the largest angle of the triangle to 1 dp.

    How would I know this without calculating the area using 1/2 a b sin(c)????
    use the law of cosines ...

     <br />
a^2 = b^2+c^2 - 2bc\cos{A}<br />

    rearrange ...

     <br />
\cos{A} = \frac{b^2+c^2-a^2}{2bc}<br />
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Mukilab View Post
    The length of the sides of a triangle are 4.2, 5.3 and 7.6.

    Calculate the size of the largest angle of the triangle to 1 dp.

    How would I know this without calculating the area using 1/2 a b sin(c)????
    Hi Mukilab,

    Use the law of cosines. Let C be the largest angle (opposite 7.6)

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