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WAEC Further Mathematics 2019 Question 17

Question 17

Trigonometry

Points X and Y are on the same horizontal base as the foot of a building such that X is 96 m due east of the building and Y is due west. If the angle of elevation of the top of the building from X is 30° and that of Y is 60°, calculate the distance of Y from the base of the building.

  1. A.30 m
  2. B.32 m
  3. C.42 m
  4. D.50 m
Show the answer and explanation

Answer: B (32 m)

Explanation

Height = 96 tan 30° ≈ 55.43 m. Distance of Y = height ÷ tan 60° = 96/3 = 32 m.