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4024/21 Oct/Nov 2021, Question 4: The Sine Rule

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

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The question, in short

Use the given village positions and distances to find an angle, a bearing, and a return-trip average speed from the travel timings.

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

Part (ai) · 4 marks

Find the size of angle PRQ using triangle PQR with PR = 3.8 km and QR = 7.5 km.

  1. 1Angle RPQ = 90 + 40 = 130°
  2. 2sin PQR = 3.8 × sin 130/7.5 = 0.3881…
  3. 3Angle PQR = 22.83…°
  4. 4Angle PRQ = 180 − 130 − 22.83… = 27.16… ≈ 27.2°

Answer27.1 to 27.2

Part (aii) · 2 marks

Determine the bearing of R as measured from Q, using the geometry of the triangle.

  1. 1Angle RPQ = 270° − 140° = 130°
  2. 2Sine rule: sin Q = 3.8 × sin 130° ÷ 7.5, so angle PQR = 22.84…°
  3. 3Bearing of P from Q = 140° + 180° = 320°
  4. 4Bearing of R from Q = 320° − 22.84…° = 297.16…°, so 297.1 to 297.2

Answer297.1 to 297.2

Part (b) · 4 marks

Given P to T is 16.5 km, outbound speed 45 km/h, a 15-minute stop, and return arrival at 11 35, find the return average speed in km/h.

  1. 1Time to T = 16.5 ÷ 45 = 0.3666… h = 22 minutes
  2. 210 30 to 11 35 = 65 minutes
  3. 3Time back = 65 − 15 − 22 = 28 minutes
  4. 4Speed = 16.5 ÷ 28 × 60 = 35.357… ≈ 35.4 km/h

Answer35.3 to 35.4

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