2009 AMC 12B Problem 16

Trapezoid ABCD has AD||BC, BD = 1, \angle DBA = 23^{\circ}, and \angle BDC = 46^{\circ}. The ratio BC: AD is 9: 5. What is CD?

\textbf{(A)}\ \frac {7}{9}\qquad \textbf{(B)}\ \frac {4}{5}\qquad \textbf{(C)}\ \frac {13}{15} \qquad \textbf{(D)}\ \frac {8}{9}\qquad \textbf{(E)}\ \frac {14}{15}

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