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WMA11/01 Jan 2024, Question 2: Triangles and Sectors in Radians

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks

The question, in short

Triangle ABC has AB = 15 cm, AC = 25 cm, angle BAC = θ° and area 100 cm². Find sin θ, then BC for θ > 90.

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

Part (a) · 2 marks

Use the given sides and area of triangle ABC to find the value of sin θ°.

  1. 1Area = ½ × AB × AC × sin θ
  2. 2100 = ½ × 15 × 25 × sin θ = 187.5 sin θ
  3. 3sin θ = 100/187.5 = 8/15

Answersin θ° = 8/15

Part (b) · 3 marks

Given θ > 90, find the length BC in cm to 3 significant figures.

  1. 1θ obtuse: θ = 180° − sin⁻¹(8/15) = 180° − 32.23° = 147.77°
  2. 2(or cos θ = −√161/15)
  3. 3BC² = 15² + 25² − 2 × 15 × 25 × cos 147.77°
  4. 4BC² = 850 + 634.4 = 1484.4
  5. 5BC = 38.5 cm (3 s.f.)

AnswerBC = 38.5 cm

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Also searched as: WMA11 January 2024 · WMA11/01 · wma11 jan24 · IAS Maths Pure Mathematics 1 January 2024 · question 2.
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