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0580/42 Feb/Mar 2024, Question 6: The Sine Rule

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

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The question, in short

Triangle ABC has AB = 17.2 cm, angle ABC = 54° and angle ACB = 68°. M is on BC with MC = 12.8 cm. Find AC, AM and the shortest distance from A to BC.

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Part (a) · 3 marks

Calculate the length AC using the given side AB and the two angles at B and C.

  1. 1AC/sin 54° = 17.2/sin 68°
  2. 2AC = 17.2 × sin 54° ÷ sin 68°
  3. 3= 15.00… ≈ 15.0 cm

Answer15.0 or 15.00 to 15.01

Part (b) · 3 marks

Using MC = 12.8 cm, calculate the length AM.

  1. 1AM² = 15.00…² + 12.8² − 2 × 15.00… × 12.8 × cos 68°
  2. 2AM² = 245.1…
  3. 3AM = 15.65… ≈ 15.7 cm

Answer15.7 or 15.65 to 15.66

Part (c) · 3 marks

Calculate the shortest distance from A to the line BC.

  1. 1Shortest distance is the perpendicular from A to BC
  2. 2Distance = 17.2 × sin 54°
  3. 3= 13.91… ≈ 13.9 cm

Answer13.9 or 13.90 to 13.92

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