What is the cosine rule?

The Cosine Rule, also known as the Law of Cosines, is a trigonometry rule that relates the lengths of a triangle's sides to the cosine of one of its angles. It's useful for solving triangles that are not right-angled. The rule is expressed as follows: In a triangle with sides of lengths a, b, and c, and with the angle opposite side c being γ (gamma), the relationship is: c^2 = a^2 + b^2 - 2ab * cos(γ) This formula can be used in various ways. If you know the lengths of all three sides, you can find the cosine of one angle, and hence the angle itself. If you know two sides and the included angle, you can find the third side's length. The Cosine Rule is an extension of the Pythagorean Theorem. When the angle γ is 90 degrees, cos(γ) becomes 0, and the formula reduces to the Pythagorean formula: c^2 = a^2 + b^2.