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Math Help - triangle area

  1. #1
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    Red face triangle area

    How do I make a function out of this problem?
    Express the area A of a 30-60-90 triangle as a function of the length h of the hypotenuse.

    The answer is (h√3)/(8).
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  2. #2
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    One side of the triangle is h cos(60) = h/2
    Another side is h sin(60) = h√3/2

    Area is 1/2 h/2 h√3/2 = h√3/8
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  3. #3
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    Label the opposite side a and the adjacent b.

    a=hsin(30), \;\ b=hcos(30)

    The formula for the area of the triangle is \frac{ab}{2}=\frac{hsin(30)\cdot hcos(30)}{2}
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  4. #4
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    Sin and Cos of angles get you the sides?
    Last edited by RaphaelB30; November 30th 2008 at 08:27 AM. Reason: Rephrase question
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  5. #5
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    Hello, RaphaelB30!

    Express the area A of a 30-60-90 triangle
    as a function of the length h of the hypotenuse.

    The answer is: \frac{h^2\sqrt{3}}{8}
    You're expected to know the ratio of the sides of a 30-60-90 right triangle.
    Code:
                  *
                 /|
                / |
               /  |
              /30|
          2a /    |  _
            /     | √3a
           /      |
          /       |
         / 60    |
        * - - - - *
             a

    We have: . 2a = h\quad\Rightarrow\quad a \:=\:\tfrac{h}{2}

    Then the base is: . a \,=\,\tfrac{h}{2}
    . . . . and the height is: . \sqrt{3}\,a \,=\,\tfrac{\sqrt{3}}{2}h

    Therefore, the area is: . A \;=\;\tfrac{1}{2}\text{(base)(height)} \;=\;\frac{1}{2}\left(\frac{h}{2}\right)\left(\fra  c{\sqrt{3}}{2}h\right) \;=\;\frac{h^2\sqrt{3}}{8}

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