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4024/12 May/Jun 2021, Question 9: Constructing Triangles

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Complete a scale drawing of triangle ABC with BA = 9 km, BC = 8 km, AC = 5 km, A due east of B, using scale 1 cm to 1 km, then find the bearing of C from B.

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

Part (a) · 2 marks

Using ruler and compasses only, construct triangle ABC at scale 1 cm to 1 km, with BA = 9 cm, BC = 8 cm and AC = 5 cm.

  1. 1Set compasses to 8 cm, draw an arc centre B
  2. 2Set compasses to 5 cm, draw an arc centre A
  3. 3C is where the arcs cross (below BA); join BC and AC

AnswerAcceptable triangle with intersecting arcs

Part (b) · 1 mark

Measure the bearing of C from B on the completed drawing.

  1. 1Angle ABC: cos B = (9² + 8² − 5²)/(2 × 9 × 8) = 120/144, so B ≈ 33.6°
  2. 2Bearing of C from B = 90 + 33.6 ≈ 124°

Answer124 (accept 122 to 126)

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