The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry. 
Home Analytic Geometry Triangle Properties of a Right Triangle  
See also: Triangle  General Definitions, Properties of Arbitrary Triangles, Altitudes of a Triangle, Isosceles Triangle, Pythagorean Theorem, Thales' Theorem, Incircle and Angle Bisectors of a Triangle, Median and Centroid of a Triangle, Ellipse  
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Properties of a Right TriangleA right triangle has one angle (the angle γ at the point C by convention) of 90 degrees (π/2). The longest side, which is opposite to the angle γ is called hypothenuse (the word derives from the Greek hypo  "under"  and teinein  "to stretch"). The legs of a right triangle (i.e. the sides adjacent to the right angle) are also known as catheti (singular: cathetus). In German, the two legs are denoted using different terms: Ankathete (adjacent cathetus) and Gegenkathete (opposite cathetus) denote the legs adjacent to and opposite the (nonright) angle in question, respectively.
The sides of the triangle are related to each other by the trigonometric functions:
sin = opposite / hypothenuse
Further the altitude of the triangle h is given by h = ab/c, the radius of the incircle is defined byr_{i} = (a + b  c)/2, the radius of the circumcircle is given byr_{cc} = c/2, and the center of gravity is at one third of the height h.If two parameters of a right triangle are known, all other parameters can be calculated. The following table contains the most important parameters (three sides a, b, c, two angles α and β and the area).


Home Analytic Geometry Triangle Properties of a Right Triangle 