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Math Help - area of triangle and sine theta.

  1. #1
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    area of triangle and sine theta.

    Area of triangle = 1/2 * product of two sides * sine angle.

    Can anyone explain the logic of having sine angle in the formula? Please explain in such a way that I don't need to memorize this formula rather derive myself.
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    Re: area of triangle and sine theta.

    area of triangle and sine theta.-non-rat.jpg

    You already know that $\displaystyle \begin{align*} A = \frac{1}{2}b\,h \end{align*}$.

    But if you look at the left-hand right-angle triangle, we can see that from the point of view of angle C, the opposite side is h and the hypotenuse is a.

    So $\displaystyle \begin{align*} \sin{(C)} = \frac{h}{a} \implies h = a\sin{(C)} \end{align*}$.

    Thus $\displaystyle \begin{align*} A = \frac{1}{2}b\,h = \frac{1}{2}a\,b\sin{(C)} \end{align*}$.
    Thanks from hisajesh
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    Re: area of triangle and sine theta.

    You are awesome!
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