catheti

Cathetus (plural catheti) is a term in Euclidean geometry referring to one of the two sides of a right triangle that form the right angle. The pair of catheti are commonly called the legs of the right triangle. The word derives from the Greek kathetós, meaning perpendicular.

In a right triangle with catheti a and b and hypotenuse c, the Pythagorean theorem holds: a^2 + b^2 = c^2. Each cathetus is perpendicular to the other and to the hypotenuse. The catheti determine the triangle’s area and serve as the base and height in standard orientation. In trigonometry, the lengths of the catheti relative to a chosen acute angle θ relate to sine and cosine: for that angle, cos θ equals the adjacent cathetus divided by the hypotenuse, sin θ equals the opposite cathetus divided by the hypotenuse, and tan θ equals the opposite cathetus divided by the adjacent cathetus.

Example: in a 3-4-5 triangle, the catheti have lengths 3 and 4, and the hypotenuse is 5. The term cathetus is largely confined to geometric discussion; in everyday language, the sides are more often referred to as the legs of the right triangle.