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.

Explanation:

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

Hence, 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.