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0580/42 Feb/Mar 2025, Question 8: Constructing Triangles

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 5 marks

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The question, in short

Use a scale drawing where 1 cm represents 0.5 km to find the real distance between boats A and B, then construct lighthouse L east of both boats.

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

Part (a) · 2 marks

Measure the distance between A and B on the drawing and convert it to actual kilometres using the scale.

  1. 1AB on the drawing = 4.2 cm
  2. 2Actual distance = 4.2 × 0.5 = 2.1 km

Answer2.1 (accept 2 to 2.2)

Part (b) · 3 marks

Using ruler and compasses only, construct L east of A and B, 4.4 km from A and 3.3 km from B, then label it.

  1. 14.4 km ÷ 0.5 = 8.8 cm and 3.3 km ÷ 0.5 = 6.6 cm
  2. 2Draw an arc of radius 8.8 cm centre A and an arc of radius 6.6 cm centre B
  3. 3Label L where the arcs cross to the east of A and B

AnswerCorrect construction for position of L with intersecting arcs 8.8 cm from A and 6.6 cm from B

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