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Math Help - P is inside an equailateral triangle

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    Newbie kira's Avatar
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    Post P is inside an equailateral triangle

    The point is inside of an equilateral triangle with side length so that the distance from to two of the sides are and . Find the distance from to the third side.
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  2. #2
    MHF Contributor
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    Go see here :
    Nick's Mathematical Puzzles: Solution 117

    Simple enough, right?
    Sum of the 3 heights = 10sqrt(3) / 2 = ~8.66
    So your missing height = ~8.66 - 1 - 3 = ~4.66
    Last edited by Wilmer; March 8th 2011 at 03:25 AM. Reason: simplify previous
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    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by kira View Post
    The point is inside of an equilateral triangle with side length so that the distance from to two of the sides are and . Find the distance from to the third side.
    the area of the equilateral triangle is immediately known. call the vertices of the equilateral triangle as A.B,C and join P to A,B and C. the triangle is subdivided into three sub-triangles out of which the area of two of the sub-triangles is known since the length of the altitudes are known. the third unknown one can be known by equating the area of the equilateral to the sum of the areas of the three sub-triangles.
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