4PM1/02 Jun 2023, Question 9: Trigonometry in 3D: Pyramids and Cones
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
For a right pyramid with regular pentagon base ABCDE, sides 2x cm and slant edges 3x cm, find the angle between plane VBC and the base, in degrees to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Let X be the centre of the base and M the midpoint of BC; angle BXC = 72°
- 2BX = x/sin 36° = 1.701x
- 3VM = √((3x)² − x²) = √8x = 2.828x
- 4MX = x/tan 36° = 1.376x
- 5cos ∠VMX = MX/VM = 1.376x/2.828x
- 6∠VMX = 60.9°
Answer60.9°
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 LemmaraMore past-paper questions on trigonometry in 3d: pyramids and cones
Also searched as: 4PM1 2 June 2023 · 4PM1/02 · 4pm1 jun23 2 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.