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Math Help - Forming Functions from Verbal Descriptions

  1. #1
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    Thumbs down Forming Functions from Verbal Descriptions

    Hey, noob here. I was wondering if any of you smarter guys out there could help me out.
    Coming from the textbook "Advanced Mathematics" by Richard Brown...

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

    TIA
    Last edited by guywhohatesmath; October 28th 2008 at 07:51 PM.
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  2. #2
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    Quote Originally Posted by guywhohatesmath View Post
    Hey, noob here. I was wondering if any of you smarter guys out there could help me out.
    Coming from the textbook "Advanced Mathematics" by Richard Brown...

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

    TIA
    1. Draw the triangle including the height h.

    2. The height divide the right angle into 60 and 30 and the hypotenuse c into 2 parts: q under the 60-angle, p under the 30-angle.

    3. The area of the right triangel is calculated by:

    A=\dfrac12\cdot c \cdot h

    4. q = h \cdot \tan(60^\circ) = h \cdot \sqrt{3}

    5. p = h \cdot \tan(30^\circ) = h \cdot \sqrt{\frac13}

    Plug in these values into the equation of the area:

    A= \dfrac12 \left(h \cdot \sqrt{3}+h \cdot \sqrt{\frac13}\right)\cdot h

    After factor out the common factor you'll get:

    A(h)=\dfrac23\sqrt{3}\cdot h^2
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  3. #3
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    Thanks for your time and help. I appreciate it.
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