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4PM1/01R Jun 2019, Question 2: The Cosine Rule

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

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The question, in short

Use triangle ABC with sides 2x, 3x and 4x cm to prove a sine value, then find x from a given area.

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

Part (a) · 4 marks

Show that sin ABC equals 3√15 ÷ 16 using the three side lengths 2x, 3x and 4x.

  1. 1cos ABC = ((2x)² + (4x)² − (3x)²)/(2 × 2x × 4x)
  2. 2= 11x²/(16x²) = 11/16
  3. 3sin² ABC = 1 − 121/256 = 135/256
  4. 4sin ABC = √135/16 = 3√15/16

Answersin ABC = 3√15/16 shown

Part (b) · 2 marks

Find x given the triangle area is 75√15 ÷ 64 cm².

  1. 1½ × 2x × 4x × 3√15/16 = 75√15/64
  2. 2(3√15/4)x² = 75√15/64
  3. 3x² = 25/16, x = 5/4 (positive root)

Answerx = 5/4

Stuck on a step? Read the free lesson: The Cosine Rule

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