10. 1 .
$$
\begin{array}{l}
\text { Given } B C^{2}-A B^{2}=8^{2}-2^{2}=10 \times 6 \\
=\left(\frac{19}{2}\right)^{2}-\left(\frac{11}{2}\right)^{2}=C D^{2}-A D^{2} \\
\Rightarrow A C \perp B D .
\end{array}
$$

Therefore, the sine value of the angle formed by the skew lines $A C$ and $B D$ is 1.
10. In the tetrahedron $ABCD$,
$$
AB=2, AD=\frac{11}{2}, BC=8, CD=\frac{19}{2} \text{.}
$$

Then the sine of the angle formed by the skew lines $AC$ and $BD$