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Math Help - I need help with a math proof

  1. #1
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    I need help with a math proof

    have to prove these two formulas are equal...

    Area of a triangle= 1/2 bc sinA

    Area of a triangle= 1/2 bh
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  2. #2
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    Hello, its.all.up.2.u!

    Prove: \text{Area of a triangle} \:=\:\tfrac{1}{2}bc \sin A
    Code:
                B
                *
               *| *
           c  * |   *   a
             *  |h    *
            *   |       *
           *    |         *
        A *  *  *  *  *  *  * C
                   b

    We know that the area is: . \text{Area} \:=\:\tfrac{1}{2}\text{(base)(height)} .[1]

    The base of the triangle is side b. .[2]

    In the right triangle at the left: . \sin A \,=\,\frac{h}{c} \quad\Rightarrow\quad h \,=\,c\sin A .[3]


    Substitute [2] and [3] into [1]:

    . . . \text{Area} \:=\:\tfrac{1}{2}\underbrace{\text{(base)}}_{b} \underbrace{\text{(height)}}_{c\sin A} \;=\;\tfrac{1}{2}bc\sin A

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