2012 AMC 10B Problem 12

Point B is due east of point A. Point C is due north of point B. The distance between points A and C is 10\sqrt 2, and \angle BAC = 45^\circ. Point D is 20 meters due north of point C. The distance AD is between which two integers?

\textbf{(A)}\ 30\ \text{and}\ 31 \qquad\textbf{(B)}\ 31\ \text{and}\ 32 \qquad\textbf{(C)}\ 32\ \text{and}\ 33 \qquad\textbf{(D)}\ 33\ \text{and}\ 34 \qquad\textbf{(E)}\ 34\ \text{and}\ 35

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