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Thread: hypotenuse help please

  1. #1
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    hypotenuse help please

    In a right triangle ABC, the legs are AB = 5 and BC = 12, and in the right triangle DEF, the hypotenuse is DE = 10, and EF = 8. Which is DF + AC?

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  2. #2
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    Quote Originally Posted by sanee66 View Post
    In a right triangle ABC, the legs are AB = 5 and BC = 12, and in the right triangle DEF, the hypotenuse is DE = 10, and EF = 8. Which is DF + AC?


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    In a right triangle the "legs" are the sides other than the hypotenuse, so in
    $\displaystyle \triangle ABC$ (by Pythagoras' theorem) $\displaystyle AC=\sqrt{5^2+12^2} = 13$.

    In $\displaystyle \triangle D E F$ we have the hypotenuse $\displaystyle DE$ is $\displaystyle 10$, and leg $\displaystyle EF=8$, so:

    $\displaystyle
    DE^2 = EF^2+DF^2,
    $

    so:

    $\displaystyle
    DF=\sqrt{10^2-8^2}=6.
    $

    RonL
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