Lemmara logoLemmaraWorked solution

4PM1/02 Jan 2023, Question 5: Trigonometry in 3D: Pyramids and Cones

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Right pyramid on a 12 cm square base, vertex above the base centre, edge EA at 30° to the base; find the height h exactly, then the angle EFO with F on AD in ratio 1:4.

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

Part (a) · 3 marks

Find the exact height h of the pyramid, using the 30° angle between edge EA and the horizontal square base.

  1. 1AC = √(12² + 12²) = 12√2, so OA = 6√2
  2. 2tan 30° = h/(6√2)
  3. 3h = 6√2 × (1/√3) = 2√6

Answerh = 2√6

Part (b) · 4 marks

Point F divides AD with AF : FD = 1 : 4; calculate angle EFO to the nearest degree.

  1. 1AF = 12/5 = 2.4, so F is 6 − 2.4 = 3.6 from the midpoint of AD
  2. 2OF = √(6² + 3.6²) = 6√34/5 ≈ 7.00
  3. 3tan EFO = EO/OF = 2√6/(6√34/5)
  4. 4∠EFO = 35°

Answer35°

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

Practise more trigonometry in 3d: pyramids and cones questions

Real 4PM1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on trigonometry in 3d: pyramids and cones

Also searched as: 4PM1 2 January 2023 · 4PM1/02 · 4pm1 jan23 2 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.