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4024/21 May/Jun 2022, Question 9: The Sine Rule

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Using bearings from A to towns B and C with AB = 300 km and AC = 280 km, work out a reverse bearing, a distance, and possible bearings of D.

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

Part (a) · 1 mark

State the bearing of A as seen from C.

  1. 1Bearing of A from C = 150 + 180
  2. 2= 330°

Answer330°

Part (b) · 4 marks

Work out the length BC.

  1. 1Angle BAC = 150 − 72 = 78°
  2. 2BC² = 300² + 280² − 2 × 300 × 280 × cos 78°
  3. 3= 168 400 − 34 929.2… = 133 470.8…
  4. 4BC = 365.3… ≈ 365 km

Answer365 or 365.3…

Part (c) · 5 marks

Given D is 145 km from B and angle ADB is 120°, determine both possible bearings of D from A.

  1. 1In triangle ABD: sin DAB/145 = sin 120°/300
  2. 2sin DAB = 145 × sin 120°/300 = 0.4185…
  3. 3Angle DAB = 24.74…°
  4. 4D can be either side of AB: 72 − 24.74… = 47.25… and 72 + 24.74… = 96.74…
  5. 5Bearings 047.3° and 096.7°

Answer047.3 or 047.25 to 047.26 and 096.7 or 096.74 to 096.75

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Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 9.
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