kateta

Kateta is a term used in geometry to denote a leg of a right triangle. It refers to either of the two sides that form the right angle, in contrast to the hypotenuse, which is the side opposite the right angle and is the triangle’s longest side. Every right triangle has exactly two catheti.

In common mathematical notation, the catheti are often labeled a and b, while the hypotenuse is labeled c. They satisfy the Pythagorean theorem, a^2 + b^2 = c^2. In trigonometry, the catheti play a key role in defining the trigonometric ratios for an acute angle: the sine of an angle equals the length of the opposite cathetus divided by the hypotenuse, while the cosine equals the adjacent cathetus divided by the hypotenuse; the tangent equals the opposite cathetus divided by the adjacent cathetus.

The term kateta appears in several languages, notably Polish, where it is the standard word for the leg of a right triangle. In English, the equivalent term is cathetus or, more descriptively, leg of a right triangle.

Applications of catheti include solving right triangles, analyzing trigonometric relationships, and problems in coordinate geometry, where the catheti correspond to horizontal and vertical differences between points. Etymology traces the word to Greek kathetos, meaning something like “placed at the side” or “perpendicular.”