Hand angle a quarter past three

On an ordinary analogue clock, how many degrees separate the hour hand from the minute hand when the time is exactly 3:15?

$7.5^\circ$. The minute hand points exactly at the 3, while the hour hand has moved a quarter of the way from 3 to 4. Each hour gap is $30^\circ$, so the gap is $\tfrac14\cdot 30^\circ=7.5^\circ$.