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4PM1/02 Jan 2020, Question 3: Trigonometry in 3D: Pyramids and Cones

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

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The question, in short

For a triangular pyramid ABCD with horizontal isosceles base ABC (AB = AC = 10 cm, BC = 16 cm), M the midpoint of BC, and face BCD isosceles with BD = CD = 26 cm, find lengths and angles.

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

Part (a) · 2 marks

Find the length of AM in cm.

  1. 1AM is perpendicular to BC and BM = 8
  2. 2AM = √(10² − 8²) = √36 = 6

AnswerAM = 6

Part (b) · 3 marks

Find the size of angle BCD in degrees, to the nearest degree.

  1. 1Triangle BCD is isosceles, so DM ⟂ BC and CM = 8
  2. 2cos ∠BCD = 8/26 = 4/13
  3. 3∠BCD = 72.07… = 72°

Answer72°

Part (c) · 4 marks

Find the size in degrees, to the nearest degree, of the angle between planes BCA and BCD.

  1. 1The angle between the planes is ∠DMA
  2. 2AD = √(26² − 10²) = 24
  3. 3tan ∠DMA = AD/AM = 24/6 = 4
  4. 4∠DMA = 75.96… = 76°

Answer76°

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