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0580/42 May/Jun 2022, Question 4: The Cosine Rule

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Use a trapezium with parallel sides, a diagonal and given lengths and angles to calculate a side, angles, another side and the area.

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

Part (a) · 3 marks

Calculate side CB using triangle DCB with DC = 6.4 cm, DB = 10.9 cm and angle CDB = 38°.

  1. 1CB² = 6.4² + 10.9² − 2 × 6.4 × 10.9 × cos 38
  2. 2CB² = 49.82…
  3. 3CB = 7.058… ≈ 7.06 cm

Answer7.06 or 7.058… or 7.059

Part (bi) · 1 mark

Work out angle ADB in triangle ADB, given angle DAB = 45° and the angle at B found from the parallel sides.

  1. 1Angle ABD = angle CDB = 38° (alternate angles)
  2. 2Angle ADB = 180 − 45 − 38 = 97°

Answer97

Part (bii) · 3 marks

Calculate side AB using triangle ADB with DB = 10.9 cm and angles now known.

  1. 1AB/sin 97 = 10.9/sin 45
  2. 2AB = 10.9 × sin 97 ÷ sin 45
  3. 3= 15.30… ≈ 15.3 cm

Answer15.3

Part (c) · 3 marks

Calculate the area of trapezium ABCD using parallel sides AB and DC = 6.4 cm and the perpendicular height.

  1. 1Height = 10.9 × sin 38 = 6.710… cm
  2. 2Area = 1/2 × (6.4 + 15.30…) × 6.710…
  3. 3= 72.81… ≈ 72.8 cm²

Answer72.8 to 72.81…

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