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0580/41 Oct/Nov 2025, Question 5: Constructing Triangles

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 5 marks

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The question, in short

Using only ruler and compasses, draw triangle ABC with AB = 8 cm, AC = 7 cm and BC = 5 cm, then use the drawing to measure angle ACB and answer scale and bearing questions about a field.

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, construct the triangle with sides 8 cm, 7 cm and 5 cm using compasses and a ruler.

  1. 1Set compasses to 7 cm and draw an arc from A
  2. 2Set compasses to 5 cm and draw an arc from B
  3. 3C is where the arcs cross; join AC and BC with a ruler

AnswerTriangle accurately completed with arcs at C.

Part (b) · 1 mark

Draw the triangle accurately on AB, then measure angle ACB with a protractor.

  1. 1Measure angle ACB with a protractor
  2. 2Check: cos C = (7² + 5² − 8²)/(2 × 7 × 5) = 10/70, so C = 81.8°

Answer80 to 85

Part (ci) · 1 mark

Given AB = 8 cm on a 1 : 10 000 scale drawing, work out the real distance from A to B in kilometres.

  1. 1AB = 8 cm on the drawing
  2. 28 × 10 000 = 80 000 cm = 800 m = 0.8 km

Answer0.8

Part (cii) · 1 mark

With B due east of A, state the bearing of A as seen from B.

  1. 1A is due west of B
  2. 2Bearing of A from B = 270°

Answer270

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Also searched as: 0580/41/O/N/25 · 0580_w25_qp_41 · 0580 w25 41 · question 5.
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