2022 AMC 12A 第 12 题

$CM$ and $DM$ are medians of equilateral faces with edge length $1$

$CM=DM=\dfrac{\sqrt3}{2}$ and $CD=1;$ apply the Law of Cosines in $\triangle CMD$

Take edge length $1.$ Since $M$ is the midpoint of $\overline{AB},$ segments $CM$ and $DM$ are altitudes of the equilateral faces, each of length $\dfrac{\sqrt3}{2}.$ Also $CD=1.$

By the Law of Cosines in $\triangle CMD,$ $$\begin{aligned} \cos(\angle CMD) &=\frac{\frac34+\frac34-1}{2\cdot\frac34} \\ &=\frac{\frac{1}{2}}{\frac{3}{2}}=\frac13. \end{aligned}$$

Thus, the correct answer is B.