3 In $\triangle A B C$, $\angle C=90^{\circ}, \angle B=30^{\circ}, A C=2, M$ is the midpoint of $A B$, and $\triangle A C M$ is folded along $C M$ so that the distance between $A$ and $B$ is $2 \sqrt{2}$. Then the distance from point $M$ to plane $A B C$ is $\qquad$.
(3 . 1 Hint: $M A=M B=M C=2$, so the projection $O$ of $M$ on plane $A B C$ is the circumcenter of $\triangle A B C$. Given $A B=2 \sqrt{2}, A C=2, B C=2 \sqrt{3}$, we know that $A B^{2}+A C^{2}=B C^{2}$, which means $\triangle A B C$ is a right triangle with the right angle at $A$. Therefore, $O$ is the midpoint of $B C$, and $M O$ is the desired length. $M O=\sqrt{M C^{2}-O C^{2}}=1$.