Geometry & Right Triangles
Right-triangle geometry is how you square a building and size a rafter.
3-4-5 (and 6-8-10, 9-12-15) = a square corner · hypotenuse = √(run² + rise²) · roof pitch = rise-in-12 (a 6:12 rises 6 in per foot) · radius = diameter ÷ 2.
Worked examples
- Legs 3 ft and 4 ft → hypotenuse 5 ft; legs 6 ft and 8 ft → 10 ft.
- A 12 ft × 16 ft rectangle’s diagonal = √(144 + 256) = √400 = 20 ft.
- A roof with a 12-ft run and 5-ft rise → rafter √(144 + 25) = 13 ft.
- A 6:12 pitch rises 6 inches per foot of run.
The 3-4-5 method is the field shortcut: measure 3 ft along one wall, 4 ft along the other, and if the diagonal between those marks is exactly 5 ft, the corner is square.
Practice: Geometry & Right Triangles
Frequently asked
What is the 3-4-5 rule?
How do you find a rafter or diagonal length?
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