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Math Help - Trapezium solving

  1. #1
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    Trapezium solving

    there is a trapezium ABCD.AB is parallel to CD.Angle A is twice of angle C.If AD=a and AB=b.Then what is the value of DC in terms of a and b?
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  2. #2
    MHF Contributor
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    Hi

    DB' = BD' = AB - AD' = b - a cos(2 alpha)
    CD = DB' + B'C = DB' + BB' / tan(alpha) = DB' + DD' / tan(alpha)
    CD = b - a cos(2 alpha) + a sin(2 alpha) / tan(alpha)
    CD = b - a (2 cosē(alpha) - 1) + a 2 sin(alpha) cos(alpha) cos(alpha) / sin(alpha)
    CD = a + b

    Of course you have also to consider the case where D' lies at the right of B
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