a² + b² = c², and what each letter must be
The theorem only applies to right triangles, and c is always the hypotenuse — the side opposite the right angle, and necessarily the longest. That is the mistake worth guarding against: plugging a leg in as c produces a negative number under the square root, which is the geometry telling you the triangle cannot exist. This page catches that rather than returning a silent error.
Rearranged for a missing leg it becomes a = √(c² − b²), which is the same relationship read backwards.
The triples worth recognising
Some right triangles have whole-number sides, and they recur constantly in textbooks and exams: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Any multiple works too — 6-8-10 is the 3-4-5 doubled — so spotting one saves you the arithmetic entirely.
The 3-4-5 is also a building-site tool: measure 3 units along one wall, 4 along the other, and if the diagonal is exactly 5 the corner is square.
Frequently asked questions
Does this work for any triangle?
No — only right triangles. For any other triangle use the law of cosines, or our triangle calculator, which solves from three sides regardless of the angles.
Is anything uploaded?
No. The triangle is drawn to scale in the page from your own numbers.
Something wrong with this tool, or an idea for it? Tell us