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0580/41 Oct/Nov 2025, Question 29: Choosing Between Sine and Cosine Rules

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 8 marks

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The question, in short

Using the given quadrilateral with diagonal AC 14 cm, sides AB 10 cm and BC 13 cm, find angle y and then the length BD.

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

Part (a) · 3 marks

Work out the size of angle y in degrees using the triangle containing AB, BC and AC.

  1. 1cos y = (10² + 14² − 13²)/(2 × 10 × 14)
  2. 2= 127/280
  3. 3y = 63.02… ≈ 63.0

Answer63.0 or 63.02 to 63.03

Part (b) · 5 marks

Find the length of BD, using the angles and sides from the diagram.

  1. 1AD/sin 38° = 14/sin 97°
  2. 2AD = 14 × sin 38° ÷ sin 97° = 8.683… cm
  3. 3Angle CAD = 180 − 97 − 38 = 45°, so angle BAD = 63.02… + 45 = 108.02…°
  4. 4BD² = 10² + 8.683…² − 2 × 10 × 8.683… × cos 108.02…°
  5. 5BD = 15.13… ≈ 15.1 cm

Answer15.1 or 15.13 to 15.14

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