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Math Help - Area of projection on a plane?

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    Area of projection on a plane?

    what is the area of the projection on a plane of an equilateral triangle 10 cm on a side, if one side is parallel to the plane and the other sides form an angle of 30 with the plane?

    *** the answer to this problem is approximately 35.35 sq. cm but i need the DIAGRAM/FIGURE of this problem and please explain the steps to solve this problem. thanks!!!
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    delete
    Last edited by Garas; January 18th 2010 at 05:42 AM.
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    Quote Originally Posted by fishlord40 View Post
    what is the area of the projection on a plane of an equilateral triangle 10 cm on a side, if one side is parallel to the plane and the other sides form an angle of 30 with the plane?

    *** the answer to this problem is approximately 35.35 sq. cm but i need the DIAGRAM/FIGURE of this problem and please explain the steps to solve this problem. thanks!!!
    Let e denote the side of the isoceles triangel which is the projection of the equilateral triangle. Let h denot the height in the isoceles triangel.

    1. e = 10\cdot \cos(30^\circ) = 5 \cdot \sqrt{3}

    2. To calculate the height h use Pythagorean theorem:

    h^2+5^2 = e^2~\implies~h^2 = (5 \cdot \sqrt{3})^2-5^2 = 50

    Thus h = 5 \cdot \sqrt{2}

    3. The area of the projection is

    A = \frac 12 \cdot 10 \cdot 5 \cdot \sqrt{2} \approx 35.355339...
    Attached Thumbnails Attached Thumbnails Area of projection on a plane?-glstg3eck_proj.png  
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