Example 2. Given the dihedral angle $\alpha-\mathrm{AB}-\beta$ is $30^{\circ}$, and there is a point $\mathrm{P}$ inside it, the distance from $\mathrm{P}$ to plane $\alpha$ is $\mathrm{PC}=3 \mathrm{~cm}$, and the distance from $\mathrm{P}$ to plane $\beta$ is $\mathrm{PD}=2 \mathrm{~cm}$. Find the distance from $\mathrm{P}$ to the edge $\mathrm{AB}$.
2. In Example 2, if the dihedral angle is $60^{\circ}$ or $135^{\circ}$, find the distance from $\mathrm{P}$ to the edge.
(Ans: $\frac{2}{3} \sqrt{57} \mathrm{~cm}$,
$\sqrt{26-12 \sqrt{2}} \mathrm{~cm})$