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    Question

    The angle of depression of vertex of a regular hexagon

    lying in a horizontal plane, form the top of a tower of height 135 m located at the centre of the regular hexagon is 60°. What is the length of the each side of the hexagon?
    A 90√3 m Correct Answer Incorrect Answer
    B 45√3 m Correct Answer Incorrect Answer
    C 45 m Correct Answer Incorrect Answer
    D 135 m Correct Answer Incorrect Answer

    Solution

    Let OX be the height of the tower, angle of depression = Angle of elevation. y is the distance between u and o. In ∆XUO tan60° = 135/y √3 = 135/y y = 135/y ⇒ 45√3 In regular hexagon, ∆UOT, ∆ SOT,..... are equilateral triangles Length of hexagon = 45√3 m

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