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0580/42 Feb/Mar 2021, Question 5: The Sine Rule

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Using the measurements in quadrilateral ABCD with diagonal BD, work out an angle at D, a side length DC, and a perpendicular distance from C to BD.

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

Part (a) · 3 marks

Find the size of angle ADB using the given side lengths in triangle ABD.

  1. 1cos ADB = (8.6² + 9.7² − 4.4²)/(2 × 8.6 × 9.7)
  2. 2= 148.69/166.84 = 0.8912…
  3. 3Angle ADB = 26.97… ≈ 27.0°

Answer27.0 or 26.97…

Part (b) · 4 marks

Find the length of side DC using triangle BCD and its given angles.

  1. 1Angle BCD = 180 − 65 − 42 = 73°
  2. 2DC/sin 65 = 9.7/sin 73
  3. 3DC = 9.7 × sin 65 ÷ sin 73
  4. 4DC = 9.192… ≈ 9.19 cm

Answer9.19 or 9.192 to 9.193

Part (c) · 3 marks

Find the shortest distance from point C to the line BD.

  1. 1The shortest distance d is perpendicular to BD
  2. 2sin 42 = d/DC
  3. 3d = 9.19… × sin 42
  4. 4d = 6.15 cm

Answer6.15 or 6.149 to 6.151…

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