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      Question

      From the top of a tower, the angle of depression of a

      car on the ground is 30°. After the car moves 40 m towards the tower in a straight line, the angle of depression becomes 45°. Find the height of the tower.
      A 10(√3 + 1) Correct Answer Incorrect Answer
      B 20(√3 + 1) Correct Answer Incorrect Answer
      C 12(√2 + 1) Correct Answer Incorrect Answer
      D 13(√3 + 5) Correct Answer Incorrect Answer

      Solution

      Let the height of the tower be h m. Let the initial horizontal distance of the car from the tower be x m. Angle of depression = angle of elevation.a Initially: tan 30° = h/x So, 1/√3 = h/x ⇒ x = h√3 ...(1) After moving 40 m towards tower, distance = x − 40. Now: tan 45° = h/(x − 40) So, 1 = h/(x − 40) ⇒ x − 40 = h ...(2) From (1) and (2): h√3 − 40 = h h(√3 − 1) = 40 h = 40/(√3 − 1) = 40(√3 + 1)/( (√3 − 1)(√3 + 1) ) = 40(√3 + 1)/2 = 20(√3 + 1)

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