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
Incircle and excircles of a triangle Because the Incenter is the same distance of all sides the trilinear coordinates for the incenter are The barycentric coordinates for a point in a triangle give weights such that the point is the weighted average of the triangle vertex positions. Barycentric coordinates for the incenter are given by where formula_7, formula_8, and formula_9 are the lengths of the sides of the triangle, or equivalently (using the law of sines) by where formula_11, formula_12, and formula_13 are the angles at the three vertices. The Cartesian coordinates of the incenter are a weighted average of the coordinates of the three vertices