Find the missing side of a right triangle using the Pythagorean theorem: a² + b² = c². Includes Pythagorean triples generator and step-by-step working.
Enter any TWO values — leave the unknown one blank. c is always the hypotenuse (longest side, opposite the right angle).
Common Right Triangles
| a | b | c | Primitive? |
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| Property | Value |
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In any right-angled triangle: a² + b² = c², where c is the hypotenuse. Named after Greek mathematician Pythagoras (~570–495 BC), though the relationship was known earlier in Babylon and China.
A Pythagorean triple is a set of three positive integers (a, b, c) satisfying a² + b² = c². The most famous is 3-4-5. A "primitive" triple has no common factor (GCD = 1). All triples can be generated from primitive ones by multiplying by an integer.
The converse is also true: if a² + b² = c², then the triangle is right-angled. This is used in construction and surveying to check right angles — the basis of the "3-4-5 rule" used by Australian builders.
The 3-4-5 rule (and its multiples: 6-8-10, 9-12-15) is widely used in Australian construction to set out perfect right angles without expensive equipment. Carpenters, builders, and landscapers rely on this daily.