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4PM1/02 Nov 2023, Question 2: Choosing Between Sine and Cosine Rules

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks

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The question, in short

Triangle ABC has AB = 3x cm, BC = 5x cm and angle ABC = 110°. Find angle BCA in degrees to one decimal place, then use the area 24 cm² to find x to 3 significant figures.

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Part (a) · 4 marks

Find the size of angle BCA in degrees, giving the answer to one decimal place.

  1. 1AC² = (3x)² + (5x)² − 2(3x)(5x)cos 110°
  2. 2AC = 6.6528…x
  3. 3sin BCA = 3x sin 110°/(6.6528…x) = 0.4237…
  4. 4∠BCA = 25.1°

Answer25.1°

Part (b) · 3 marks

Given the triangle's area is 24 cm², find the value of x to 3 significant figures.

  1. 124 = (1/2)(3x)(5x)sin 110°
  2. 2x² = 48/(15 sin 110°)
  3. 3x = 1.85

Answerx = 1.85

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