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4PM1/01 Jun 2022, Question 3: Choosing Between Sine and Cosine Rules

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks

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The question, in short

Calculate the area of shaded triangle BCE in rectangle ABCD with AB = 10 cm, AD = 15 cm, DE = 13 cm, angle BAE = 35°, angle AED obtuse.

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Solution · 7 marks

  1. 1Angle DAE = 90° − 35° = 55°
  2. 2Sine rule in triangle AED: sin E/15 = sin 55°/13 ⇒ E = 70.9° or 109.1°; AED obtuse so E = 109.1°
  3. 3Angle ADE = 180° − 55° − 109.1° = 15.9°
  4. 4Distance of E from AD: h = 13 sin 15.9° = 3.57 cm
  5. 5Distance of E from BC = 10 − 3.57 = 6.43 cm
  6. 6Area BCE = (1/2) × 15 × 6.43 = 48.2 cm²

Answer48.2 cm²

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