##### Definition:

Law of cosines is a trigonometry law which says about the relation between the sides of a triangle to one of its angle. It is used to calculate the third side of the triangle from the length of two side of the triangle and an angle in between those sides.

#### Formula:

a =√b^{2} + c^{2} - 2bc cos A
b =√a^{2} + c^{2} - 2ac cos B
c =√a^{2} + b^{2} - 2ab cos C
##### Example:

In triangle ABC, side b = 12, side c = 2 and A = 45^{o}.Find side a to the nearest integer.

##### Given,

Side b = 12
Side c = 2
A = 45 ^{o}

##### To find,

Formula to find side a = √b^{2} + c^{2} - 2bc cos A

##### Solution:

a =√12^{2} + 2^{2} - 2(12)(2) cos(45)
a =√544 - 252.154
a =√291.845
a =17.83
Therefore, the side a = 17 (Rounded to nearest integer)