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Rebuilding civilization

Geometry and measurement

Right triangle (Pythagoras)

Hypotenuse, legs and angles of a right triangle; check square corners with the 3-4-5 rule.

m
m

Result

Hypotenuse
m
Leg a
m
Leg b
m
Angle opposite leg a
°
Angle opposite leg b
°
Area

How it is calculated

Pythagorean theorem: hypotenuse² = a² + b². If you know the hypotenuse h and one leg a: b = √(h² − a²).

3-4-5 rule to set out a right angle on site: mark 3 m on one side and 4 m on the other; the corner is square when the diagonal measures exactly 5 m. Any multiple works (6-8-10, 0.9-1.2-1.5).

Keep in mind

  • When setting out a house, also check that both diagonals of the rectangle are equal.
  • Other useful whole-number triples: 5-12-13 and 8-15-17.

See also