What is the formula for Cos C in the Law of Cosines?

The correct formulation of the Law of Cosines is given by the expression that relates the sides of a triangle to the cosine of one of its angles. Specifically, in the context of the Law of Cosines, the formula for Cos C is derived from the general structure of the equation, which establishes a relationship between the sides of the triangle and the cosine of an angle.

The main formula being highlighted, where c represents the length of the side opposite angle C, and a and b refer to the lengths of the other two sides, is structured as follows: c² = a² + b² - 2ab Cos C. From this equation, it can be rearranged to isolate Cos C. By doing so, the equation expresses Cos C in terms of the sides of the triangle, thus allowing us to calculate the cosine of angle C.

To derive Cos C from the original Law of Cosines formula, you would rearrange the equation like this:

1. Begin with c² = a² + b² - 2ab Cos C.

2. Rearrange it to isolate the term involving Cos C:

2ab Cos C = a² + b² - c².

3. Finally, divide both sides by 2