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4MA1/1H Jan 2020, Question 14: The Cosine Rule

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Parallelogram EFGH has EF = 9.3 cm, FG = 14.7 cm and angle EFG = 106°. Find its area and the diagonal EG, each to 3 significant figures.

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

Part (a) · 2 marks

Calculate the area of the parallelogram using the given side lengths and included angle, giving the result to 3 significant figures.

  1. 1Area of a parallelogram = ab sin C
  2. 2Area = 9.3 × 14.7 × sin 106°
  3. 3= 131.4…, so 131 cm² to 3 s.f.

Answer131

Part (b) · 3 marks

Calculate the length of diagonal EG of the parallelogram, giving the answer to 3 significant figures.

  1. 1EG² = 9.3² + 14.7² − 2 × 9.3 × 14.7 × cos(106)
  2. 2EG² = 86.49 + 216.09 − 2 × 9.3 × 14.7 × (−0.2756)
  3. 3EG² = 86.49 + 216.09 + 75.3
  4. 4EG² = 377.88
  5. 5EG = √377.88
  6. 619.4

Answer19.4

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