This topic summary covers Knowledge Organiser: 3D Trigonometry within 3D Trigonometry for GCSE Mathematics. Revise 3D Trigonometry in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 2 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: 3D Trigonometry
Key Terms
- Space diagonal: The longest diagonal through a 3D solid
- Angle of elevation: Angle measured upward from horizontal
- Angle of depression: Angle measured downward from horizontal
- Right-angled triangle in 3D: A 2D triangle extracted from a 3D shape
Must-Know Facts
- Every 3D problem is really a series of 2D problems — extract the right triangles
- Draw each 2D right-angled triangle separately and label sides clearly
- Often need to find the base diagonal first as a stepping stone
- Use Pythagoras for distances; use SOHCAHTOA for angles
- Space diagonal: d = √(x² + y² + z²)
Key Methods
- Angle with base: tan θ = height ÷ base diagonal
- Space diagonal: d = √(x² + y² + z²)
- Step 1: find base diagonal; Step 2: use with height
- Always state which triangle you are working with
Key Formulas
- Space diagonal: d = √(l² + w² + h²)
- Angle with base: tan θ = h ÷ base diagonal
- Base diagonal (cuboid): √(l² + w²)
- Same SOHCAHTOA rules apply — identify the right-angled triangle first
Common Mistakes
- Not finding base diagonal first: Must apply Pythagoras twice — base diagonal then space diagonal/angle
- Using wrong triangle: Sketch the 3D shape and clearly identify the right-angled triangle being used
- Rounding intermediate values: Keep full calculator accuracy until the final answer to avoid compounding errors
- Angle with wrong side: The angle with the base uses the perpendicular height and the base diagonal — not a slant edge
Practice questions for 3D Trigonometry
To find the angle between a line and a horizontal plane in a 3D problem, which technique is typically used?
Describe the general method for finding the angle between a line and a plane in a 3D problem.
Quick recall flashcards
Key Strategy for 3D Trig
Find the right-angled triangles hidden in the 3D shape. Often you need to find the BASE DIAGONAL first!
3D Pythagoras Formula
d² = x² + y² + z² for a space diagonal through a cuboid with dimensions x, y, z