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 measures of a 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.
Let's understand the concept.
Let's observe the triangle ABC with angles A, B and C and sides a, b and c as shown below.
The Law of Cosines (also called the Cosine Rule) states that:
c2 = a2 + b2 − 2ab cos(C)
Different cosine formulas
As per the law of cosines formula, to find the length of sides of say △ABC, we can use the following:
- a2 = b2 + c2 – 2bc cos A
- b2 = a2 + c2 – 2ac cos B
- c2 = b2 + a2 – 2ba cos C