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4PM1/02 Jan 2022, Question 4: Trigonometry in 3D: Cuboids

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 9 marks

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The question, in short

For a cube ABCDEFGH with 10 cm edges, calculate a diagonal length, an angle at a vertex, and the obtuse angle between two planes.

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

Part (a) · 2 marks

Find the exact length of FC in cm.

  1. 1FC² = 10² + 10² + 10²
  2. 2FC = √300 = 10√3 cm

AnswerFC = √300 = 10√3 cm

Part (b) · 2 marks

Find the size of angle FCA in degrees to one decimal place.

  1. 1AC = √(10² + 10²) = √200
  2. 2cos ∠FCA = AC/FC = √200/√300
  3. 3∠FCA = 35.264…° = 35.3°

Answer35.3°

Part (c) · 5 marks

Find the obtuse angle between planes BFH and BHC, to the nearest degree.

  1. 1Let X be the midpoint of BH
  2. 2CX = √200/2 = √50
  3. 3FX = √(50 + 100) = √150
  4. 4cos FXC = (150 + 50 − 300)/(2 × √150 × √50)
  5. 5∠FXC = 125.26…° = 125°

Answer125°

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