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4PM1/02R Jun 2020, Question 3: The Cosine Rule

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 8 marks

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The question, in short

Triangle ABC has AB = 10 cm, AC = 12 cm; D on BC with BD = 6 cm and DC = 2 cm, AD = x cm. Prove x = 11, then find the area of triangle ADB in cm² to 3 significant figures.

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

Part (a) · 4 marks

Using the given side lengths, demonstrate that the length AD equals 11 cm.

  1. 1Triangle ABC: cos B = (10² + 8² − 12²)/(2 × 10 × 8) = 20/160
  2. 2Triangle ABD: cos B = (10² + 6² − x²)/(2 × 10 × 6) = (136 − x²)/120
  3. 320/160 = (136 − x²)/120
  4. 4x² = 121 ⇒ x = 11

Answerx = 11 shown

Part (b) · 4 marks

Calculate the area of triangle ADB, giving your answer in cm² correct to 3 significant figures.

  1. 1cos B = 1/8 ⇒ angle ABD = 82.8…°
  2. 2Area = ½ × 10 × 6 × sin 82.8…°
  3. 3= 29.8 cm²

Answer29.8 cm²

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