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JAMB Mathematics 2006 Question 30

Question 30

Trigonometry

In triangle XYZ, ∠XYZ = 15°, ∠XZY = 45° and |XY| = 7cm. Find |YZ|.

  1. A.14√2cm
  2. B.(7/2)√6cm
  3. C.7√2cm
  4. D.7cm
Show the answer and explanation

Answer: B ((7/2)√6cm)

Explanation

∠YXZ = 180° − 15° − 45° = 120°. By the sine rule, YZ = 7 × sin 120°/sin 45° = 7 × (√3/2)/(√2/2) = 7√6/2.