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WAEC Mathematics 2019 Question 24

Question 24

Trigonometry

In XYZ, |YZ| = 32 cm, ∠YXZ = 52° and ∠XZY = 90°. Find, correct to the nearest centimetre, |XZ|.

Diagram for this question
  1. A.31 cm
  2. B.25 cm
  3. C.20 cm
  4. D.13 cm
Show the answer and explanation

Answer: B (25 cm)

Explanation

YZ is opposite the 52° angle and XZ is next to it, so tan 52° = 32/|XZ|. |XZ| = 32 ÷ 1.2799 ≈ 25 cm.