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0580/22 Feb/Mar 2025, Question 18: Using Trigonometry and Pythagoras Together

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 9 marks

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The question, in short

Using the diagram with AC = 17 cm, AE = 18 cm, BD = 6 cm and angle EAB = 60°, work with triangles ABE and BCD to prove CD and find the perimeter of ACDE.

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

Part (a) · 5 marks

Show, using the right-angled triangle BCD and the given lengths, that CD equals 10 cm.

  1. 1cos 60° = AB/18, so AB = 18 × 0.5 = 9 cm
  2. 2BC = 17 − 9 = 8 cm
  3. 3CD² = 8² + 6² = 64 + 36 = 100
  4. 4CD = √100 = 10 cm

Answer√100 = 10

Part (b) · 4 marks

Calculate the perimeter of quadrilateral ACDE, giving the result in the form p + k√q.

  1. 1BE = 18 sin 60° = 18 × √3/2 = 9√3
  2. 2DE = 9√3 − 6
  3. 3Perimeter = 18 + 17 + 10 + 9√3 − 6
  4. 4= 39 + 9√3 cm

Answer39 + 9√3

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