# Law of Cosines Trigonometry

** Law of cosines or Cos law **

The law of cosines or Cos law is one of the trigonometric laws which is useful for solving the angles or sides of a triangle.

For example, if all three sides of a triangle (SSS) are given, the cosine rule allows one to easily find any of the angle measures.

Similarly, if two sides and the angle between them is known, the cosine laws can be used to calculate the third side of the triangle.

**The law of Cosines Definition**

The cosine rule, is also known as the law of cosines or Cosine Formula, relates all three sides of a triangle with an angle of a triangle.

**Law of Cosines Formula**

If we want to find the length of sides of a triangle ABC, we can write as,

**a ^{2 }= b^{2 }+ c^{2 }– 2bc Cos A**

**b ^{2 }= a^{2 }+ c^{2 }– 2ac Cos B**

**c ^{2 }= a^{2 }+ b^{2 }– 2ab Cos C**

To find the angles of a triangle ABC, then cosine rules are written as,

**Cos A = (b ^{2 }+ c^{2 }– a^{2})/2bc **

**Cos B = (a ^{2 }+ c^{2 }– b^{2})/2ac **

**Cos C = (a ^{2 }+ b^{2 }– c^{2})/2ab**

** Where a, b and c are lengths of sides of triangle ABC.**