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0580/43 Oct/Nov 2021, Question 6: The Cosine Rule

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 13 marks

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The question, in short

Use quadrilateral ABCD with diagonal AC, sides AB 11 cm, BC 8 cm, AC 12 cm, angles ADC 100° and ACD 50° to find lengths, angles and areas.

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

Part (a) · 3 marks

Find side AD using the triangle with angles 100° and 50° and side AC 12 cm.

  1. 1AD/sin 50° = 12/sin 100°
  2. 2AD = 12 × sin 50° ÷ sin 100°
  3. 3= 9.334… ≈ 9.33 cm

Answer9.33 or 9.334...

Part (b) · 4 marks

Find angle BAC in the triangle with sides 11 cm, 8 cm and 12 cm, showing it rounds to 40.42°.

  1. 18² = 11² + 12² − 2 × 11 × 12 × cos BAC
  2. 2cos BAC = (121 + 144 − 64)/264 = 201/264 = 0.7613…
  3. 3Angle BAC = 40.415… ≈ 40.42°

Answer40.415...

Part (c) · 3 marks

Work out the total area of quadrilateral ABCD by combining the two triangles.

  1. 1Angle CAD = 180 − 100 − 50 = 30°
  2. 2Area ACD = 1/2 × 12 × 9.334… × sin 30° = 28.00…
  3. 3Area ABC = 1/2 × 12 × 11 × sin 40.415…° = 42.78…
  4. 4Area ABCD = 28.00… + 42.78… = 70.79… ≈ 70.8 cm²

Answer70.8 or 70.77 to 70.79...

Part (d) · 3 marks

Find the perpendicular distance from B to the diagonal AC.

  1. 1Shortest distance is perpendicular to AC
  2. 2Distance = 11 × sin 40.415…°
  3. 3= 7.131… ≈ 7.13 cm

Answer7.13 or 7.131 to 7.132...

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Also searched as: 0580/43/O/N/21 · 0580_w21_qp_43 · 0580 w21 43 · question 6.
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