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    Question

    The angle of depression from the top of a light-house

    of two boats are 60° and 30° towards the west, if the two boats are 60m apart, then the height of the light house is
    A 20√2 m Correct Answer Incorrect Answer
    B 30√3 m Correct Answer Incorrect Answer
    C 40√3 m Correct Answer Incorrect Answer
    D 50√3 m Correct Answer Incorrect Answer

    Solution

    D = h (cotA - cotB) Here (h = height of light house) D = AB = 60 60 = h (cot30° - cot60°) 60 = h (√3-1/√3) 60 = h ((3-1)/√3) 2h/√3 = 60 m         h = 60 × √3/2  = 30√3 m So height of the tower is = 30√3 m

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