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0580/12 May/Jun 2023, Question 22: Pythagoras' Theorem

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 6 marks

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The question, in short

Use two right-angled triangle diagrams to calculate a side length: find AB in triangle ABC, then find PR using triangles PQS and PRS.

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

Part (a) · 2 marks

In right-angled triangle ABC with AC = 8.6 cm and angle ACB = 42°, calculate the length AB.

  1. 1sin 42 = AB/8.6
  2. 2AB = 8.6 × sin 42
  3. 3= 5.754… ≈ 5.75 cm

Answer5.75 or 5.754 to 5.755

Part (b) · 4 marks

With PQ = 23.8 cm, QS = 11.2 cm and SR = 20 cm, and PS perpendicular to QR, calculate PR.

  1. 1PS² = 23.8² − 11.2²
  2. 2PS² = 566.44 − 125.44 = 441, so PS = 21
  3. 3PR² = 21² + 20² = 441 + 400 = 841
  4. 4PR = √841 = 29 cm

Answer29

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