The angle at a quarter past three
On an ordinary analog clock, what is the angle, in degrees, between the hour hand and the minute hand at 3:15?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
The hour hand is not exactly on the 3 at 3:15.
The hour hand moves 30 degrees per hour, so 0.5 degree per minute.
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. The minute hand points exactly at the 3, but the hour hand has moved a quarter of the way from the 3 to the 4.
Step 1: the minute hand. At 15 minutes it points at the 3: 90 degrees from 12.
Step 2: the hour hand. It moves degrees per hour. At 3:15 it is at degrees.
Step 3. The angle is degrees.
In general. At hours and minutes, the angle is degrees (or 360 minus that, whichever is smaller). The trap is to answer 0.