Explanation

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c². The hypotenuse (c) is always the longest side, opposite the right angle.

Applications: finding unknown side lengths, checking if angles are 90°, calculating distances. Pythagorean triples (3-4-5, 5-12-13, 8-15-17) give integer solutions.

Only works for right triangles. For other triangles, use the cosine rule: c² = a² + b² – 2ab·cos(C). Pythagoras is a special case where C = 90° and cos(90°) = 0.