2012 AMC 10B Question 12 - thichhoctoan.com

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

$ 30$ and $ 31 $
$ 31$ and $ 32 $
$ 32$ and $ 33 $
$ 33$ and $ 34 $
$ 34$ and $ 35 $