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JAMB Mathematics 1978 Question 45

Question 45

Trigonometry

The angle of elevation of the top of a vertical tower from a point A on the ground is 60°. From a point B, 2 units of distance further away from the foot of the tower, the angle of elevation of the top of the tower is 45°. Find the distance of A from the foot of the tower.

  1. A.3 + √3
  2. B.5 + √3
  3. C.3 − √3
  4. D.1 + √3
  5. E.√3 − 1.
Show the answer and explanation

Answer: D (1 + √3)

Explanation

If A is x from the foot, the height is x tan 60° = x√3 and also (x + 2) tan 45° = x + 2. So x(√3 − 1) = 2 and x = 2/(√3 − 1) = √3 + 1.