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4MA1/2HR Jan 2023, Question 23: Choosing Between Sine and Cosine Rules

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

Chords AEC and BED of a circle meet at E, with AE = x + 5, BE = x, CE = 5x − 12, DE = x + 12 cm and angle DAE = 48°. Find angle ADE to one decimal place.

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

Solution · 5 marks

  1. 1Intersecting chords: AE × CE = BE × DE
  2. 2(x + 5)(5x − 12) = x(x + 12)
  3. 35x² + 13x − 60 = x² + 12x
  4. 44x² + x − 60 = 0
  5. 5(4x − 15)(x + 4) = 0
  6. 6x = 3.75 or x = −4, and a length cannot be negative, so x = 3.75
  7. 7AE = 3.75 + 5 = 8.75 cm and DE = 3.75 + 12 = 15.75 cm
  8. 8Sine rule in triangle ADE: sin(ADE) ÷ AE = sin(DAE) ÷ DE
  9. 9sin(ADE) = 8.75 × sin48° ÷ 15.75
  10. 10sin(ADE) = 0.4129
  11. 11ADE = 24.4°

Answer24.4

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