Ms. cooper tells her geometry class to draw a triangle with with side lengths 4.2 cm and 3.0 cm with a 52° angle between them. what will be the measure of the third side?

One way to solve this (a SAS problem) is to use the Law of Cosines, which states: 
c² = a² + b² + 2ab *cos(A),
where a and b are our known sides, angle A is our known angle, and c is the side we want to find
Plugging in:
c² = 4.2² + 3² + 2(4.2)(3)(cos(52°)
c²= 17.64 + 9 + 25.2 (.62)
c² = 42.15
c = 6.5

Answer is 6.5 cm