Lemmara logoLemmaraWorked solution

4MA1/1HR Jun 2020, Question 17: Trigonometry in 3D: Cuboids

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

For a prism with square base EFGH of side 12 cm, vertical edges DE = CH = 10 cm and AD = BC = 15 cm, find an angle and a length.

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

Part (a) · 3 marks

Find the angle that CF makes with the plane of the square base EFGH, rounded to one decimal place.

  1. 1FH = √(12² + 12²) = √(288) = 16.97...
  2. 2tan(CFH) = 10 / 16.97...
  3. 3CFH = arctan(10 / 16.97...) = 30.5

Answer30.5

Part (b) · 3 marks

Calculate the distance from B to E, giving the result to one decimal place.

  1. 1BG = 10 + √(15² − 12²) = 10 + √(81) = 10 + 9 = 19
  2. 2FH = √(12² + 12²) = 16.97...
  3. 3BE = √(19² + 16.97...²) = √(361 + 288) = √(649) = 25.5

Answer25.5

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 Lemmara

More past-paper questions on trigonometry in 3d: cuboids

Also searched as: 4MA1 1HR June 2020 · 4MA1/1HR · 4ma1 jun20 1hr · question 17.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.