Recognize and isolate c^2 onto one side of the equation cos C = a^2 + b^2 -c^22ab.
c^2 = a^2 + b^2 - 2abcos C
We want to complete the given sentence.
The standard form of the Law of Cosines for cos C = a^2 + b^2 -c^22ab is .
The form of the Law of Cosines given in the statement is called the alternative form. It allows us to find the cosine of an angle using the side lengths.
Alternative Form
cos A = b^2 + c^2 - a^2/2bc
cos B = a^2 + c^2 - b^2/2ac
cos C = a^c + b^2 - c^2/2ab
The standard form of the Law of Cosines is equivalent to the alternative form. The equation in the standard form is useful to find the square of a triangle's side in terms of two other side measures and the cosine of an angle opposite to this side.
cos C = a^c + b^2 - c^2/2ab
There is cos C in the given equation. Therefore, the standard form of this equation should have c^2 isolated on the left-hand side. Let's do it!
