23. Given a regular triangular prism $A B C-A_{1} B_{1} C_{1}$ with each edge length being $a$, a plane $M$ is constructed through $A B_{1}$ and is parallel to $B C_{1}$.
(1) Find the dihedral angle $\alpha$ ($\alpha < 90^{\circ}$) formed between plane $M$ and plane $A B C$,
(2) Find the distance from point $A_{1}$ to plane $M$.
23. $\alpha=\operatorname{arctg} 2$.
The distance from $A_{1}$ to the plane $M$ is $\frac{\sqrt{5}}{5} a$.