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Math Help - lake triangle - need help

  1. #1
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    lake triangle - need help

    Determine how many acres there would be in that triangular lake, surrounded as shown by square plots of 370, 116 and 74 acres
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by sonia1 View Post
    Determine how many acres there would be in that triangular lake, surrounded as shown by square plots of 370, 116 and 74 acres

    A=\sqrt{s(s-a)(s-b)(s-a)}

    a=19.23538

    b=10.77033

    <br />
c=8.60233

    s=\frac{a+b+c}{2} = \frac{\sqrt370 + \sqrt116 +\sqrt74}{2} = 19.30402

    A=\sqrt{19.30402(0.06864)(8.53368)(10.70169)}=11.0  0037=11
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  3. #3
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    how do u prove it

    do u know how to work it out another way instead of using that formula..the long way
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  4. #4
    Member TheMasterMind's Avatar
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    Quote Originally Posted by sonia1 View Post
    do u know how to work it out another way instead of using that formula..the long way
    \frac{1}{4} (\sqrt116+\sqrt74+\sqrt370)(\sqrt116+\sqrt74+\sqrt  370)^{1/2}
    \frac{1}{4}         (\sqrt116+\sqrt370-\sqrt74)(\sqrt74+\sqrt370-\sqrt116)^{1/2}

    Can you take it from here? This way is very long. Are you sure you need to long way?
    Last edited by TheMasterMind; December 22nd 2008 at 02:04 PM.
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  5. #5
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    Hello, sonia1!

    There is another approach . . . It requires Trig . . .


    Determine how many acres there would be in a triangular lake,
    surrounded by square plots of 370, 116 and 74 acres.
    Code:
                                  *
                              *    *
                 ___      *         *   __
                √116  *              * √74 
                  *                   *
              *                        *
        A *     *     *     *     *     * 
                        √370
    Use the Law of Cosines to find angle A.

    . . \cos A \:=\:\frac{(\sqrt{116})^2 + (\sqrt{370})^2 - (\sqrt{74})^2} {2(\sqrt{116})(\sqrt{370})} \:=\:0.994345617

    Hence: . A \:\approx\:6.1^o


    Then the area of the triangle is given by:

    . . A \;=\;\tfrac{1}{2}(\sqrt{116})(\sqrt{370})\sin6.1^o \:=\:11.007643903 \;\approx\;11\text{ acres}

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  6. #6
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    thanks

    hi thanks for your help
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