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JAMB Mathematics 1979 Question 50

Question 50

Trigonometry

A man is standing on the corridor of a 10 storey building and looking down at a tall tree in front of the building. He sees the top of the tree at an angle of depression of 30°. If the tree is 200m tall and the man's eyes are 300m above the ground, calculate the angle of depression of the foot of the tree as seen by the man.

  1. A.30°
  2. B.60°
  3. C.45°
  4. D.75°
  5. E.90°
Show the answer and explanation

Answer: B (60°)

Explanation

The top of the tree is 100m below his eyes, so the horizontal distance is 100/tan 30° = 100√3m. For the foot, tan θ = 300/(100√3) = √3, so θ = 60°.