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Math Help - estimating percentage increase

  1. #1
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    estimating percentage increase

    A triangle had two sides of length a and b with an include angle measuring Pi/3 radians. Given that a increases by 5%, b decreases by 6% and the included angle increases by 2%, estimate the percentage increase of area of the triangle.

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  2. #2
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    e^(i*pi)'s Avatar
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    Re: estimating percentage increase

    The area of a triangle is A = \dfrac{1}{2}ab \sin(C)

    A_1 = \dfrac{ab\sqrt{3}}{4} \text{ .... (eq 1)}

    A_1(1+x) = \dfrac{1}{2}(1.05a)(0.94b)\sin\left(\dfrac{1.02\pi  }{3}\right) \text{ .... (eq 2)}

    If we tidy up the constants in equation 2 we get 0.4935ab\sin\left(\dfrac{1.02\pi}{3}\right) \text{ .... (eq 3)}


    Divide eq3 by eq1 to isolate 1+x and then take 1 to get the answer in decimal form which will need changing to percentage
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  3. #3
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    Re: estimating percentage increase

    i divided equation 3 by eqn 1 which gave me :

    A1(1+x)/A1=0.998717

    but i don't get where to go from there?
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  4. #4
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    Re: estimating percentage increase

    You can cancel A1: 1+x = 0.998717
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  5. #5
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    Re: estimating percentage increase

    but that doesn't correspond to the answer give, which is 0.21%
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