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WMA11/01 Jun 2022, Question 2: The Ambiguous Case of the Sine Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks

The question, in short

Triangle ABC has AB = 21 cm, BC = 13 cm, angle BAC = 25° and angle ACB = x°. Find sin x° and then x, using the sine rule.

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

Part (a) · 2 marks

Apply the sine rule to calculate sin x°, giving the result to 4 decimal places.

  1. 1sin x°/21 = sin 25°/13
  2. 2sin x° = 21 sin 25°/13 = 0.6827

Answersin x° = 0.6827

Part (b) · 3 marks

Given AB is the longest side, determine x in degrees to 2 decimal places.

  1. 1sin⁻¹(0.6827) = 43.05°
  2. 2AB is the longest side, so angle ACB (opposite AB) is the largest angle and must be obtuse
  3. 3x = 180° − 43.05° = 136.95

Answerx = 136.95

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