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0580/41 May/Jun 2021, Question 5: The Cosine Rule

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 11 marks

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The question, in short

Triangle ABC with a point X on BC: from two lengths at X and two given angles, use trigonometry to find AC, BX and the area.

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

Part (a) · 4 marks

Use the cosine rule in triangle AXC to find AC.

  1. 1Angle AXC = 180 − 78 = 102°
  2. 2AC² = 10.6² + 6.4² − 2 × 10.6 × 6.4 × cos 102°
  3. 3AC² = 181.5…
  4. 4AC = 13.47… ≈ 13.5 cm

Answer13.5 or 13.47…

Part (b) · 4 marks

Use the sine rule in triangle ABX to find BX.

  1. 1Angle BAX = 180 − 58 − 78 = 44°
  2. 2BX/sin 44° = 10.6/sin 58°
  3. 3BX = 10.6 × sin 44° ÷ sin 58° = 8.682… ≈ 8.68 cm

Answer8.68 or 8.682 to 8.683

Part (c) · 3 marks

Find the area of the whole triangle ABC.

  1. 1BC = 8.682… + 6.4 = 15.08…
  2. 2Area = 1/2 × 10.6 × 15.08… × sin 78°
  3. 3= 78.19… ≈ 78.2 cm²

Answer78.2 or 78.17 to 78.19…

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Also searched as: 0580/41/M/J/21 · 0580_s21_qp_41 · 0580 s21 41 · question 5.
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