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4024/21 Oct/Nov 2020, Question 3: The Sine Rule

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

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The question, in short

Construct triangle PQR with PR = 7.5 cm and QR = 6 cm on the given line PQ, then find its area; for the two-triangle diagram use AB = 9.7, BC = 6.4, CD = 3.8, AC = 5.3 and angle ADC = 63° to find angles.

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

Part (ai) · 2 marks

Using ruler and compasses only, construct triangle PQR with PR = 7.5 cm and QR = 6 cm, starting from the drawn line PQ.

  1. 1PQ is 8 cm: open compasses to 7.5 cm, draw an arc centred on P
  2. 2Open compasses to 6 cm, draw an arc centred on Q
  3. 3R is where the arcs cross; join PR and QR

AnswerCorrect triangle with intersecting arcs

Part (aii) · 2 marks

Measure suitable lengths on your constructed triangle and use them to calculate the area of triangle PQR.

  1. 1Draw the perpendicular from R to PQ and measure it: height ≈ 5.3 cm
  2. 2Area = 1/2 × 8 × 5.3 = 21.2 cm²

Answer20.8 to 21.6

Part (bi) · 3 marks

In the diagram with CD = 3.8 cm, AC = 5.3 cm and angle ADC = 63°, calculate angle DAC.

  1. 1sin DAC/3.8 = sin 63/5.3
  2. 2sin DAC = 3.8 × sin 63 ÷ 5.3 = 0.6388…
  3. 3Angle DAC = 39.70…°

Answer39.7 or 39.70...

Part (bii) · 3 marks

Using AB = 9.7 cm, BC = 6.4 cm and AC = 5.3 cm, calculate angle ABC.

  1. 1cos ABC = (6.4² + 9.7² − 5.3²)/(2 × 6.4 × 9.7)
  2. 2= (40.96 + 94.09 − 28.09)/124.16 = 106.96/124.16
  3. 3Angle ABC = 30.51…° ≈ 30.5°

Answer30.5 or 30.51 to 30.52

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Also searched as: 4024/21/O/N/20 · 4024_w20_qp_21 · 4024 w20 21 · question 3.
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