This is a SAS triangle (two sides and an included angle) so we can use the Law of Cosines to find the length of side D:

\(D^{2}=E^"{2}+F^{2}−2EF\cos\theta\)

\(D^{2}=4^{2}+7^{2}-2(4)(7)\cos50^{\circ}\)

\(D^{2}=65-56\cos50^{\circ}\)

\(D=\sqrt{65-56\cos50^{\circ}}\)

\(D \sim 5.4 cm\)