1972 AHSME Problem 14

A triangle has angles of 30^\circ and 45^\circ. If the side opposite the 45^\circ angle has length 8, then the side opposite the 30^\circ angle has length

\textbf{(A) }4\qquad \textbf{(B) }4\sqrt{2}\qquad \textbf{(C) }4\sqrt{3}\qquad \textbf{(D) }4\sqrt{6}\qquad \textbf{(E) }6

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.