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    Question

    The length of the shadow of a vertical tower increases

    by 9 m on horizontal ground when the height of the sun changes from 45° to 30 ° , then find the height of the tower?
    A 9(√3 - 1) Correct Answer Incorrect Answer
    B 9(√3 + 1)/2 Correct Answer Incorrect Answer
    C 9(√3 - 1)/2 Correct Answer Incorrect Answer
    D 9√3 Correct Answer Incorrect Answer

    Solution

    AB = 9 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/(9 + x) 1/ √3 = h/(9 + h) 9 + h = √3 h √3 h - h = 9 h ( √3 - 1 ) = 9 h = 9/( √3 - 1)x ( √3 + 1)/ ( √3 + 1) = 9( √3 + 1)/2

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