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    Question

    The length of the shadow of a vertical tower increases

    by 8 m on horizontal ground when the height of the sun changes from 45° to 30 ° , then find the height of the tower?
    A 8(√3 - 1) Correct Answer Incorrect Answer
    B 4(√3 + 1) Correct Answer Incorrect Answer
    C 4(√3 - 1) Correct Answer Incorrect Answer
    D 8√3 Correct Answer Incorrect Answer

    Solution

    AB = 8 m DC = h, BC = x  In   ∆BCD tan 45 ° = DC/BC = h/x 1 = h/x x = h In  ∆ACD  tan 30° = DC/AC = DC/(AB + BC) 1/ √3  = h/(8 + x)  1/ √3  = h/(8 + h)  8 + h =  √3 h √3 h - h = 8 h ( √3 - 1 ) = 8 h = 8/( √3 - 1) x  ( √3 + 1)/ ( √3 + 1) =   4( √3 + 1)

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