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OAU Post-UTME Mathematics 2017 (Set 1 Type 1) Question 10

Question 10

Trigonometry

In a triangle ABC, if AB = 15cm and angle ABC = 45° while angle AĈB = 60°, find the length of line AC

  1. A.15√6 cm
  2. B.10√6 cm
  3. C.20√6 cm
  4. D.5√6 cm
Show the answer and explanation

Answer: D (5√6 cm)

Explanation

Sine rule: AC/sin 45° = 15/sin 60°. AC = 15 × (√2/2) ÷ (√3/2) = 15√2/√3 = 5√6 cm.