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4PM1/01 Jun 2019, Question 3: The Sine Rule

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 6 marks

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The question, in short

Triangle ABC has AC = 7 cm, BC = 10 cm and angle BAC = 65°. Find angle ABC to the nearest 0.1° and the triangle's area in cm² to 3 significant figures.

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Part (a) · 3 marks

Use the given sides and angle to find angle ABC, giving the answer to the nearest 0.1°.

  1. 1sin B/7 = sin 65°/10
  2. 2sin B = 7 sin 65°/10 = 0.6344…
  3. 3B = 39.37… = 39.4°

Answer39.4°

Part (b) · 3 marks

Calculate the area of triangle ABC in cm², correct to 3 significant figures.

  1. 1Angle ACB = 180° − 65° − 39.37° = 75.63°
  2. 2Area = ½ × 10 × 7 × sin 75.63°
  3. 3= 33.90… = 33.9 cm²

Answer33.9 cm²

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