MA30-08 Maths Coming soon
Pythagoras' theorem in three dimensions
MA30-08
This lesson is coming soon.
In this lesson
Identify the right-angled triangle embedded within a 3D solid and apply Pythagoras' theorem to find a missing length, choosing the most efficient triangle rather than a longer multi-step route.
What it covers
- Identify a right-angled triangle hidden inside a cuboid (e.g. the space diagonal)
- Identify a right-angled triangle hidden inside a pyramid (e.g. apex to a base midpoint)
- Choose the most direct, efficient right-angled triangle to isolate, rather than chaining through unnecessary intermediate triangles
- Never substitute an estimated or measured-looking value for an intermediate length - always calculate it
Key words
For: AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560, Edexcel IGCSE 4MA1, Cambridge IGCSE 0580
On the specification
| Board | Spec | Statement |
|---|---|---|
| AQA GCSE 8300 | G20 | Know the formulae for: Pythagoras’ theorem, a² + b² = c² and the trigonometric ratios, sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse and tanθ = opposite/adjacent |
| Edexcel GCSE 1MA1 | G20 | Know the formulae for: Pythagoras’ theorem a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two-dimensional figures |
| Eduqas GCSE C300 | HG20 | Know the formulae for: Pythagoras' theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent, apply them to find angles and lengths in right-angled triangles in two dimensional figures and, where possible, general triangles in two and three dimensional figures |
| OCR GCSE J560 | 10.05a | Know, derive and apply Pythagoras' theorem a^2 + b^2 = c^2 to find lengths in right-angled triangles in 2D figures. |
| Edexcel IGCSE 4MA1 | H4.8D | Use Pythagoras' theorem in three dimensions |
| Cambridge IGCSE 0580 | E6.6 | Carry out calculations and solve problems in three dimensions using Pythagoras' theorem and trigonometry, including calculating the angle between a line and a plane. |
For teachers
This GCSE Maths lesson teaches Pythagoras' theorem in three dimensions. By the end, students should be able to identify the right-angled triangle embedded within a 3D solid and apply Pythagoras' theorem to find a missing length, choosing the most efficient triangle rather than a longer multi-step route. It works through two worked examples and the mistakes examiners report.