Clock Hands

An analog clock shows the time as 3:15. What is the angle between the hour and minute hands?

Solution

The hour hand will move 360 degrees in 12 hours, so that's 30 degrees per hour, which is 7.5 degrees per 15 minutes. So at 3:15, the hour hand is at 97.5 degrees when the minute hand is at 90 degrees. So the angle between them is 7.5 degrees.