The Pythagorean theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides. Mathematically, it's written as \(a^2 + b^2 = c^2\). This relationship helps determine the distance between points or the length of an unknown side when the other two are known. It’s widely used in fields like architecture, navigation, and physics to solve problems involving distances and measurements in right-angled triangles.