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HomeCIE IGCSE MathematicsTrigonometry: Trigonometry in 3D — angles and lengths in solids
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Trigonometry: Trigonometry in 3D — angles and lengths in solids
Practice Questions

20 CIE IGCSE Mathematics questions on Trigonometry: Trigonometry in 3D — angles and lengths in solids, each with instant feedback and a full examiner-style mark scheme.

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✨ Revision guide includes key terms, worked examples and exam technique for Trigonometry: Trigonometry in 3D — angles and lengths in solids.

Try 2 sample questions on Trigonometry: Trigonometry in 3D — angles and lengths in solids

Question 1 · 1 mark · Difficulty 1/3

A surveyor is calculating the angle of elevation from a point on level ground to the top of a building. The building stands on a rectangular plot. From a corner of the plot, the horizontal distance to the base of the building is 40 m and the building is 30 m tall. What is the angle of elevation to the nearest degree?

  1. 37°
  2. 41°
  3. 49°
  4. 53°
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✓ Answer: A37°
Award 1 mark for tan θ = 30/40 = 0.75, θ = tan⁻¹(0.75) = 36.87° ≈ 37°. B is incorrect — this results from an arithmetic error. C is incorrect — this confuses opposite and adjacent sides. D is incorrect — this uses sin⁻¹(30/40) instead of tan⁻¹.
Question 2 · 1 mark · Difficulty 1/3

A warehouse in Singapore has a roof in the shape of a triangular prism. The cross-section is an isosceles triangle with base 12 m and slant edges 10 m each. What is the vertical height of the triangular cross-section?

  1. 6 m
  2. 8 m
  3. √136 m
  4. √64 m
Show answer & explanation
✓ Answer: B8 m
Award 1 mark for using Pythagoras on half the isosceles triangle: h² + 6² = 10², h² = 100 - 36 = 64, h = 8 m. A is incorrect — this is half the base, not the height. C is incorrect — this adds instead of subtracting in Pythagoras. D is incorrect — while √64 = 8, the question asks for the evaluated answer.
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CIE IGCSE Mathematics: Trigonometry: Trigonometry in 3D — angles and lengths in solids FAQ

How many CIE IGCSE Mathematics questions on Trigonometry: Trigonometry in 3D — angles and lengths in solids are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Trigonometry: Trigonometry in 3D — angles and lengths in solids for CIE IGCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real CIE paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for CIE IGCSE students preparing for Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Trigonometry: Trigonometry in 3D — angles and lengths in solids practice with other Mathematics topics or even switch to a totally different CIE subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Trigonometry: Trigonometry in 3D — angles and lengths in solids questions aligned to the official CIE IGCSE Mathematics syllabus?
Every question is written against the published CIE IGCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CIE paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from CIE.
How is Trigonometry: Trigonometry in 3D — angles and lengths in solids typically tested on CIE IGCSE Mathematics papers?
Trigonometry: Trigonometry in 3D — angles and lengths in solids appears across multiple question types on real CIE IGCSE Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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