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0580/43 May/Jun 2022, Question 10: Trigonometry in 3D: Cuboids

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 7 marks

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The question, in short

Cuboid ABCDEFGH has CG = 6 cm, diagonal AG = 24 cm and AB = 2BC. Find AB and the angle between AG and base ABCD.

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Part (a) · 4 marks

Using CG = 6 cm, AG = 24 cm and AB = 2BC, calculate the length AB.

  1. 1AC² = AG² − CG² = 24² − 6² = 540
  2. 2Let BC = x, AB = 2x: (2x)² + x² = 540
  3. 35x² = 540, x² = 108, x = 10.39…
  4. 4AB = 2 × 10.39… = 20.78… ≈ 20.8 cm

Answer20.8 or 20.76 to 20.79

Part (b) · 3 marks

Calculate the angle that the space diagonal AG makes with the base ABCD.

  1. 1The angle is GAC, with CG = 6 opposite and AG = 24 hypotenuse
  2. 2sin GAC = 6/24
  3. 3Angle = 14.47… ≈ 14.5°

Answer14.5 or 14.47 to 14.48

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