Suppose a triangle has two sides of the length 2and 3 and that the angle between these two sides is 60 what is the length of the third side of the triangle

Let the given sides be "a" and "b" and the unknown side be "c". The Law of Cosines tells you

... c^2 = a^2 + b^2 - 2ab*cos (C)

... c^2 = 2^2 + 3^2 - 2*2*3*cos (60°)

... c^2 = 7

... c = √7 ≈ 2.6458

The third side of the triangle is √7, about 2.6458.