In a right triangle, the cathetus (originally from the Greek word Κάθετος; plural: catheti), commonly known as a leg, is either of the sides that are adjacent to the right angle. It is occasionally called the periphrasis ("side about the right angle"). The side opposite the right angle is the hypotenuse. When referring to the hypotenuse, the catheti are often referred to simply as "the other two sides".
If the catheti of a right triangle have different lengths, distinction can be made between the minor (shorter) and major (longer) cathetus. The ratio of the lengths of the catheti defines the trigonometric functions tangent and cotangent of the angles in the triangle. In a right triangle, the length of the cathetus is also the geometric mean between the length of the segment cut by the altitude to the hypotenuse and the length of the whole hypotenuse.
By the Pythagorean theorem, the sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse.
- Bernhardsen, T. Geographic Information Systems: An Introduction, 3rd ed. New York: Wiley, p. 271, 2002.
- Cathetus at Encyclopaedia of Mathematics
- Weisstein, Eric W., "Cathetus", MathWorld.
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