Trigonometry angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined, except for similarity, by the angles. Once the angles are known, the ratios of the sides are determined, regardless of the overall size of the triangle. If the length of one of the sides is known, the other two are determined. These ratios are given by the following trigonometric functions of the known angle "A", where "a", " b" and "c" refer to the lengths of the sides in
Right triangle legs can be expressed in terms of the inradius and the other leg as A triangle "ABC" with sides formula_13, semiperimeter "s", area "T", altitude "h" opposite the longest side, circumradius "R", inradius "r", exradii "r", "r", "r" (tangent to "a", "b", "c" respectively), and medians "m", "m", "m" is a right triangle if and only if any one of the statements in the following six categories is true. All of them are of course also properties of a right triangle, since characterizations are equivalences. The trigonometric functions for acute angles can be defined as ratios of the sides of