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4024/22 May/Jun 2025, Question 22: The Cosine Rule

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 9 marks

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The question, in short

Calculate fencing rolls and shortest distance for triangle ABC with AB = 150 m, BC = 187 m, angle ABC = 112°.

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

Part (a) · 5 marks

Find AC using the cosine rule, then work out how many 20 m rolls cover the perimeter.

  1. 1AC² = 150² + 187² − 2 × 150 × 187 × cos 112°
  2. 2= 78484.4…
  3. 3AC = 280.15… m
  4. 4Perimeter = 280.15… + 150 + 187 = 617.15… m
  5. 5617.15… ÷ 20 = 30.857…, so 31 rolls

Answer31

Part (b) · 4 marks

Calculate the perpendicular distance from B to side AC using area or trigonometry.

  1. 1Area = 1/2 × 150 × 187 × sin 112° = 13003.7… m²
  2. 2Shortest distance h is perpendicular to AC: 1/2 × 280.15… × h = 13003.7…
  3. 3h = 150 × 187 × sin 112° ÷ 280.15…
  4. 4= 92.83… ≈ 92.8 m

Answer92.8 to 92.9…

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