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4PM1/01 Jun 2020, Question 3: Trigonometry in 3D: Pyramids and Cones

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 9 marks

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The question, in short

For a right pyramid with rectangular base 12 cm by 16 cm and vertical height 14 cm, find a sloping edge length and two angles involving edge AE and face AED.

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

Part (a) · 3 marks

Find the length of one sloping edge such as EA, giving the result to 3 significant figures.

  1. 1AC = √(12² + 16²) = 20, so AM = 10
  2. 2AE = √(14² + 10²) = √296
  3. 3= 17.20… ≈ 17.2 cm

Answer17.2 cm

Part (b) · 3 marks

Find the angle that edge AE makes with the horizontal base, in degrees to one decimal place.

  1. 1The angle is ∠EAM
  2. 2tan ∠EAM = EM/MA = 14/10
  3. 3∠EAM = 54.46… ≈ 54.5°

Answer54.5°

Part (c) · 3 marks

Find the angle between the triangular face AED and the horizontal base, in degrees to one decimal place.

  1. 1Let X be the midpoint of AD; MX = ½ × CD = 8
  2. 2The angle is ∠EXM
  3. 3tan ∠EXM = 14/8
  4. 4∠EXM = 60.25… ≈ 60.3°

Answer60.3°

Stuck on a step? Read the free lesson: Trigonometry in 3D: Pyramids and Cones

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