The Law of Cosines is a fundamental relation in triangle geometry that provides a connection between the lengths of the sides of a triangle and the cosine of one of its angles. For triangle ABC, where ‘a’, ‘b’, and ‘c’ represent the lengths of the sides opposite to angles A, B, and C respectively, the law of cosines can be expressed as follows:
- a² = b² + c² – 2bc * cos(A) (relating side a to sides b and c and angle A)
- b² = a² + c² – 2ac * cos(B) (relating side b to sides a and c and angle B)
- c² = a² + b² – 2ab * cos(C) (relating side c to sides a and b and angle C)
In essence, this formula allows you to find the length of one side of the triangle if you know the lengths of the other two sides and the measure of the angle between them. Conversely, if you know all three sides, you can use the law of cosines to find the angles of the triangle. It’s particularly useful in non-right triangles, where the Pythagorean theorem doesn’t apply.