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0580/43 May/Jun 2021, Question 9: Choosing Between Sine and Cosine Rules

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

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The question, in short

Use the quadrilateral diagram with DB = 14 cm and the given angles to find its perimeter, then work with a cube whose space diagonal AB = 8.5 cm.

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

Part (a) · 7 marks

Calculate the perimeter of quadrilateral ABCD using diagonal DB = 14 cm, right angle at A, and angles 35°, 45°, 60°.

  1. 1AB = 14 cos 35° = 11.468…, AD = 14 sin 35° = 8.030…
  2. 2Angle BCD = 180 − 45 − 60 = 75°
  3. 3BC = 14 sin 60°/sin 75° = 12.552…
  4. 4DC = 14 sin 45°/sin 75° = 10.248…
  5. 5Perimeter = 11.468 + 8.030 + 12.552 + 10.248 = 42.298… ≈ 42.3 cm

Answer42.3 or 42.28 to 42.30...

Part (bi) · 3 marks

Find the edge length of the cube given its diagonal AB = 8.5 cm.

  1. 1l² + l² + l² = 8.5²
  2. 23l² = 72.25, l² = 24.083…
  3. 3l = √24.083… = 4.907… ≈ 4.91 cm

Answer4.91 or 4.907...

Part (bii) · 3 marks

Find the angle between diagonal AB and the base of the cube.

  1. 1The vertical edge (4.907…) is opposite the angle, AB is the hypotenuse
  2. 2sin θ = 4.907…/8.5 = 0.5773…
  3. 3θ = 35.26… ≈ 35.3°

Answer35.3 or 35.26 to 35.3

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