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      Question

      From a point on the ground, the angle of elevation of

      the top of a tower is 30 degrees. After moving 10√3 m towards the tower, the angle becomes 60 degrees. The height of the tower is:
      A 12 m Correct Answer Incorrect Answer
      B 15 m Correct Answer Incorrect Answer
      C 17 m Correct Answer Incorrect Answer
      D 23 m Correct Answer Incorrect Answer

      Solution

      Let the nearer distance from tower be x m. Height = x tan 60 = x√3 From the farther point: distance = x + 10√3 Height = (x + 10√3) tan 30 = (x + 10√3)/√3 So, x√3 = (x + 10√3)/√3 3x = x + 10√3 2x = 10√3 x = 5√3 Height = x√3 = 5√3 x √3 = 15

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