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0580/22 Feb/Mar 2022, Question 21: Trigonometry in 3D: Cuboids

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 7 marks

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The question, in short

Calculate angles and lengths in a 3D open box using a stick resting diagonally through it, given AB = 18.6 cm, BC = 9 cm, CG = 14.5 cm.

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

Part (a) · 4 marks

Calculate the angle the stick makes with the base of the box.

  1. 1The angle is GAC, with AC in the base
  2. 2AC² = 18.6² + 9² = 426.96, AC = 20.66… cm
  3. 3tan GAC = 14.5/20.66…
  4. 4Angle GAC = 35.05… ≈ 35.1°

Answer35.1 or 35.05 to 35.06

Part (b) · 3 marks

Given AM = 30 cm, show that GM = 4.8 cm to 1 decimal place.

  1. 1AG² = 18.6² + 9² + 14.5² = 637.21
  2. 2AG = 25.24… cm
  3. 3GM = 30 − 25.24… = 4.75… cm
  4. 4= 4.8 cm to 1 decimal place

Answer4.75 to 4.78…

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