Final answer:
The Law of Cosines relates the side lengths and one angle of any triangle, generalizing the relationship given by the Pythagorean theorem for non-right triangles.
Step-by-step explanation:
For any triangle ABC with side lengths a, b, and c opposite the angles A, B, and C, respectively, the Law of Cosines gives the relationship between the sides of the triangle and one of its angles. The Law of Cosines is an extension of the Pythagorean theorem, where the Pythagorean theorem applies to right-angled triangles with the relationship a² + b² = c², and the square root form, c = √(a² + b²). For a non-right angled triangle, the Law of Cosines is given by c² = a² + b² - 2ab * cos(C), which relates side c with sides a and b and the angle opposite to side c, that is, angle C.