4MA1/2HR Jun 2023, Question 22: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Cuboid problems: find a space diagonal length in one cuboid, and an angle involving a line and a midpoint in another cuboid.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Cuboid ABCDEFGH has AB = 15 cm, BC = 4 cm, CF = 9 cm. Find BE to 3 significant figures.
- 14² + 9² = 16 + 81 = 97
- 297 + 15² = 97 + 225 = 322
- 3√(322) = 17.944...
- 417.9
Answer17.9
Part (b) · 3 marks
Cuboid PQRSTUVW has PR = 42 cm, angle between PU and plane PQRS is 30°, M is midpoint of PR. Find angle UMR to 3 significant figures.
- 1UR = 42 × tan(30) = 42 × (1/√(3)) = 24.248...
- 2M is midpoint of PR, so MR = 42 / 2 = 21
- 3tan(angle UMR) = UR / MR = 24.248... / 21 = 1.1547...
- 4angle UMR = arctan(1.1547...) = 49.106...
- 549.1
Answer49.1
Stuck on a step? Read the free lesson: Trigonometry in 3D: Cuboids
Practise more trigonometry in 3d: cuboids questions
Real 4MA1 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: cuboids
Also searched as: 4MA1 2HR June 2023 · 4MA1/2HR · 4ma1 jun23 2hr · question 22.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.