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 using the side lengths of the triangle relative to the perimeter—i.e., using the barycentric coordinates given above, normalized to sum to unity—as weights. (The weights are positive so the incenter lies inside the triangle as stated above.) If the three vertices are located at formula_14, formula_15, and formula_16, and the sides opposite these vertices have corresponding lengths formula_7, formula_8, and formula_9, then the incenter is at Denoting the incenter of triangle "ABC" as "I", the distances from the incenter to the vertices combined with the lengths of the triangle sides obey the equation Additionally, where "R" and "r" are the