Law of Sines/ Cosines

The Law of Sines establishes a relationship between the angles and the side lengths of triangle ABC. In total there are three sines. Another important relationship between the side lengths and the angles of a triangle is expressed by the Law of Cosines. The expression itself involves a single cosine, but by rotation or symmetry similar formulas are valid for other angles. Also cosine unlike sine changes, it's sign in the range from 0 degrees to 180 degrees of valid angles of a triangle. Sine is always positive in this range, cosine is positive up to 90 degrees where it becomes zero and is negative afterwards.