1983 AHSME Problem 19

Point D is on side CB of triangle ABC. If \angle{CAD} = \angle{DAB} = 60^\circ\text{, }AC = 3\text{ and }AB = 6, then the length of AD is

\textbf{(A)} \ 2 \qquad \textbf{(B)} \ 2.5 \qquad \textbf{(C)} \ 3 \qquad \textbf{(D)} \ 3.5 \qquad \textbf{(E)} \ 4

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