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WMA11/01 Oct 2023, Question 5: The Sine Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

Use the roof-frame diagram with BD = x, CD = 1 + x, BC = 5 and angle BCD = θ to prove a cosine result, then find the area of triangle ABC.

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

Part (a) · 2 marks

Show that cos θ° equals (13 + x) divided by (5 + 5x), using the sides of triangle BCD.

  1. 1Cosine rule in triangle BCD: cos θ = (BC² + CD² − BD²)/(2 × BC × CD)
  2. 2= (25 + 1 + 2x + x² − x²)/(10(1 + x))
  3. 3= (26 + 2x)/(10 + 10x)
  4. 4= (13 + x)/(5 + 5x)

AnswerShown: cos θ = (25 + (1 + x)² − x²)/(10(1 + x)) = (26 + 2x)/(10 + 10x) = (13 + x)/(5 + 5x)

Part (b) · 5 marks

With x = 2√3, angle BAC = 30° and ADC straight, find the area of triangle ABC in m² to one decimal place.

  1. 1x = 2√3: cos θ = (13 + 2√3)/(5 + 10√3) = 0.7377…, so θ = 42.47°
  2. 2Angle ABC = 180 − 30 − 42.47 = 107.53°
  3. 3Sine rule: AB/sin 42.47° = 5/sin 30°, so AB = 6.752 m
  4. 4Area = (1/2) × 5 × 6.752 × sin 107.53°
  5. 5= 16.1 m² (1 d.p.)

Answer16.1 m²

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Also searched as: WMA11 October 2023 · WMA11/01 · wma11 oct23 · IAS Maths Pure Mathematics 1 October 2023 · question 5.
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