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Math Help - Finding a triangles angles from its area + 2 sides?

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    Finding a triangles angles from its area + 2 sides?

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    Last edited by SarahGr; May 14th 2009 at 07:31 PM.
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  2. #2
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    Hello, SarahGr!

    A triangle had area of 21 cm² and two of its sides are 9 cm and 14cm long.
    Find the possible measures of the angle formed by these sides?

    I know the formula for the area of a triangle is ½abSin(C)
    but i have no idea how to do this one.

    The formula is: . \tfrac{1}{2}ab\sin C \:=\:\text{Area}

    We are given: . a = 9,\:b = 14,\:\text{Area} = 21

    Plug them in! . . . \tfrac{1}{2}(9)(14)\sin C \:=\:21 \quad\Rightarrow\quad \sin C \:=\:\frac{1}{3}

    Then: . C \;=\;\sin^{-1}\left(\tfrac{1}{3}\right) \;\approx\;19.5^o,\:160.5^o

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    Last edited by SarahGr; May 14th 2009 at 07:31 PM.
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