The length of side UV is 13.86 inches.
To find the measure of side UV, we can use the sine function. We know that the sine of 60 degrees is 0.866. We also know that the length of side WV is 12. We can set up the following proportion:
sin 60 degrees / UV = WV / UW
0.866 / UV = 12 / UW
UW = (12 * UV) / 0.866
UW = 13.86
Therefore, the length of side UV is 13.86 inches.