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4024/22 Oct/Nov 2025, Question 4: Constructing Triangles

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 3 marks

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The question, in short

Given side lengths AB = 8.5 cm, AC = 6 cm and BC = 7 cm, construct triangle ABC with ruler and compasses on the provided segment AB, then measure angle BAC.

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

Part (a) · 2 marks

On the given line AB, use ruler and compasses only to build triangle ABC with AC = 6 cm and BC = 7 cm.

  1. 1Set compasses to 6 cm, draw an arc centred at A
  2. 2Set compasses to 7 cm, draw an arc centred at B
  3. 3Where the arcs cross is C; join AC and BC with a ruler (keep the arcs)

AnswerCorrect triangle with intersecting arcs

Part (b) · 1 mark

Draw triangle ABC accurately on side AB using ruler and compasses only, then find the size of angle BAC.

  1. 1Measure angle BAC with a protractor
  2. 2Check by cosine rule: cos A = (8.5² + 6² − 7²)/(2 × 8.5 × 6) = 59.25/102, so angle BAC ≈ 54°

Answer54.5 (accept 53 to 56)

Stuck on a step? Read the free lesson: Constructing Triangles

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