For triangle ABC with sides a, b, and c the law of cosines states the following.
The Law of cosine helps in finding the unknown measure of the triangle.
Answer: The law of cosine states that when all three sides of a triangle are given, we can easily find all the possible angles of the triangle.
Go through the explanation to understand better.
a, b, c are the sides of the triangle and C is the angle opposite to the side c of the triangle.
The Law of Cosines (also called the Cosine Rule) says:
c2 = a2 + b2 − 2ab cos(C)
Significance of the law of cosines
The law of cosine signifies the relation between the length of the side of the triangle with respect to the cosine of its angle, which is nothing but what we also term as the law of cosines.
Different cosine formulas
As per the cosines law formula, to find the length of sides of triangle say △ABC, we can write as;
- a2 = b2 + c2 – 2bc cos α
- b2 = a2 + c2 – 2ac cos β
- c2 = b2 + a2 – 2ba cos γ