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WMA11/01 Jan 2019, Question 7: The Ambiguous Case of the Sine Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

A question on the ambiguous case of the sine rule.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

  1. 1Sine rule in triangle ABC: sin ACB / 6.5 = sin 35° / 4.7
  2. 2sin ACB = 0.7932…, giving 52.5° or 127.5°
  3. 3From the figure, angle ACB is obtuse, so ∠ACB = 127.5°

Answer127.5°

Part (b) · 3 marks

  1. 1Angle ABC = 180° − 35° − 127.5° = 17.5°; AC = 4.7 sin 17.5° / sin 35° = 2.46 m
  2. 2Triangle BCD is isosceles: angle BCD = 52.5°, so CD = 2 × 4.7 cos 52.5° = 5.72 m
  3. 3AD = 2.46 + 5.72 = 8.19 m
  4. 4Total = 8.19 + 6.5 + 4.7 + 4.7 = 24.1 m, which is 24 m to the nearest metre

Answer24 m (total 24.1 m)

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