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      Question

      The angle of elevation of the top of a tower from the

      top of a building whose height is 680 m is 45° and the angle of elevation of the top of same tower from the foot of the same building is 60°. What is the height (in m) of the tower?
      A 340(3 + √3) Correct Answer Incorrect Answer
      B 310(3 - √3) Correct Answer Incorrect Answer
      C 310(3 + √3) Correct Answer Incorrect Answer
      D 340(3 - √3 Correct Answer Incorrect Answer

      Solution

      ATQ, Let AB be the tower and CD  Be the building (680m) and E Be the point  Then, BE = 680m AE = h and CE = BD = 6 Then, (h/6) = tan 45° = 1 h=6 then, (h + 680m)/6 = tan 60° = √3 (h + 680m) = √3 b (h + 680m) = √3 h (√3 - 1) h = 2 (340) (√3 - 1)h/340 = (√3 - 1) (√3 + 1) (√3 - 1) is common and cancelled out from both sides h = (√3 + 1) 340 

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