AMC 12 2009b 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} \textbf{(B)}\ \frac {4}{5} \textbf{(C)}\ \frac {13}{15} \textbf{(D)}\ \frac {8}{9} \textbf{(E)}\ \frac {14}{15}