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
