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4PM1/01 Nov 2021, Question 7: Area of a Triangle Using Sine

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 9 marks

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The question, in short

Triangle with sides 6 cm, 8 cm and k cm: write cos θ in terms of k, then use the area √455 cm² to find the two possible values of k.

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

Part (a) · 2 marks

Cosine rule rearranged for cos θ.

  1. 1Cosine rule: k² = 6² + 8² − 2(6)(8)cos θ°
  2. 2cos θ° = (36 + 64 − k²)/96
  3. 3cos θ° = (100 − k²)/96

Answercos θ° = (100 − k²)/96 shown

Part (b) · 7 marks

Use the area to find sin θ, then cos θ, then k.

  1. 1√455 = (1/2)(6)(8)sin θ°, so sin θ° = √455/24
  2. 2cos²θ° = 1 − 455/576 = 121/576
  3. 3cos θ° = ±11/24
  4. 411/24 = (100 − k²)/96 gives k² = 56, k = √56
  5. 5−11/24 = (100 − k²)/96 gives k² = 144, k = 12

Answerk = √56 (= 2√14 ≈ 7.48) or k = 12

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