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} meters, and \angle B A C=45^{\circ}. Point D is 20 meters due north of point C. The distance A D is between which two integers?

**Answer Choices**

A. 30 and 31

B. 31 and 32

C. 32 and 33

D. 33 and 34

E. 34 and 35