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      Question

      A vertical tower stands on a horizontal plane and is

      surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of the bottom of the flag staff is and that of the top of the flag staff is β. Then the height of the tower is
      A h tan α Correct Answer Incorrect Answer
      B htanα / (tan β−tanα) Correct Answer Incorrect Answer
      C htanα / (tanα−tan β) Correct Answer Incorrect Answer
      D None of these Correct Answer Incorrect Answer

      Solution

      Apply tan   in ∆BCD Tan   = x / K k = (x / tan ) ---- (1) apply tanβ in ∆ACD => tanβ = (ĥ+x) / K => K = (h + x) / (tanβ) ----- (2) Example like (1) and (2) => x / tan   = (h+x) / tanβ => xtanβ = tan h + xtan => xtanβ – xtan   = h tan => x(tanβ – tan ) = h tan => x = (h tan2) / (tanβ – tan )

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