Setting out
3–4–5 setting-out triangle
- where
- sides of the 3-4-5 triangle (m)
- scale factor (m)
Explain this equation
This scales the classic 3–4–5 triangle to a convenient size for setting out a right angle on site, such as a corner of a building or an extension.
k is the scale factor in metres. a = 3k and b = 4k are the two legs measured along the lines that should be at right angles. c = 5k is the diagonal between the ends of those legs.
Because 3² + 4² = 9 + 16 = 25 = 5², Pythagoras says a triangle with sides in the ratio 3:4:5 must have a right angle between the two shorter sides. Multiplying all three by the same k keeps the shape, and so the right angle, unchanged.
With k = 1 the sides are 3, 4 and 5 m; with k = 2 they are 6, 8 and 10 m. Doubling k doubles every side.
Watch out: measure both legs from the same corner point. A bigger triangle reduces the effect of small tape errors, so use the largest one the site allows.
Scale a right-angle check to a useful site size.
Enter your values to see the result.
Good to know
Measure from the same corner and use the same units. Larger triangles usually reduce the effect of small reading errors.
Sources
- Geometry / arithmetic
Estimates are not design approval or British Standards compliance checks. Structural arch, retaining-wall, wind, foundation, lintel and masonry-capacity design are not performed. Use the project engineer’s specification.