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4024/21 Oct/Nov 2025, Question 20: The Cosine Rule

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Triangular field ABC with AB = 65 m, AC = 75 m and angle CAB = 125°; find side BC, angle ABC and the shortest distance from A to BC.

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Part (a) · 3 marks

Use the two given sides and included angle 125° to show BC = 124.3 m to 1 decimal place.

  1. 1BC² = 65² + 75² − 2 × 65 × 75 × cos 125°
  2. 2= 4225 + 5625 + 5592.4… = 15 442.4…
  3. 3BC = √15 442.4… = 124.267… = 124.3 m (1 d.p.)

Answer124.26 to 124.27

Part (b) · 3 marks

Calculate the size of angle ABC using the given triangle dimensions.

  1. 1sin ABC/75 = sin 125°/124.3
  2. 2sin ABC = 75 × sin 125° ÷ 124.3 = 0.4942…
  3. 3Angle ABC = 29.62… ≈ 29.6°

Answer29.6 or 29.59 to 29.64

Part (c) · 3 marks

Calculate the shortest distance from vertex A to the side BC.

  1. 1Shortest distance is the perpendicular from A to BC
  2. 2Distance = 65 × sin 29.62…°
  3. 3= 32.12… ≈ 32.1 m

Answer32.1 or 32.09 to 32.15

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