In a
right triangle, a cathetus (originally from the
Greek word ; plural: catheti), commonly known as a leg, is either of the sides that are adjacent to the
right angle
In geometry and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the ad ...
. It is occasionally called a "side about the right angle". The side opposite the right angle is the
hypotenuse. In the context of the hypotenuse, the catheti are sometimes referred to simply as "the other two sides".
If the catheti of a right triangle have equal lengths, the triangle is
isosceles. If they have different lengths, a 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
acute angles in the triangle: the ratio
is the tangent of the acute angle adjacent to
and is also the cotangent of the acute angle adjacent to
.
In a right triangle, the length of a cathetus is the
geometric mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...
of the length of the adjacent segment cut by the
altitude to the hypotenuse and the length of the whole hypotenuse.
By the
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...
, the sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse.
The term leg, in addition to referring to a cathetus of a right triangle, is also used to refer to either of the equal sides of an
isosceles triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter versio ...
or to either of the non-parallel sides of a
trapezoid.
In architecture, the term cathetus has been used for the eye of the
volute. It was so termed because its position is determined, in an
Ionic (or voluted)
capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used f ...
, by a line let down from the point in which the volute generates.
References
External links
* Bernhardsen, T. ''Geographic Information Systems: An Introduction'', 3rd ed. New York: Wiley, p. 271, 2002.
''Cathetus'' at Encyclopaedia of Mathematics* {{MathWorld , urlname=Cathetus , title=Cathetus
Parts of a triangle