When an analog clock reads 3:15, what's the angle(in degrees) between the hour hand and the minute hand?

Question

When an analog clock reads 3:15, what's the angle(in degrees) between the hour hand and the minute hand?

Answer 1

On an analog clock, 3:xx means that the hour hand is pointing just past the 3.  Since the hour hand moves 360° in 12 hours, that is 30° in one hour, or 7.5° in 15 minutes.

 

The minute hand is pointing to the 3 (for 15 minutes) since it moves 360^° in 60 minutes.  That is, 90° in 15 minutes.

 

The minute hand is pointing at 90° and the hour hand is pointing at 97.5° (measured clockwise from 12 meaning 0°).

  The difference is 7.5°.

Answer 2

A clock face with12 numbers divides a

circle into 12 sets of 30 degrees each.

 

15 minutes past 3:00 is 1/4 of the

hour between 3 and 4 o'clock.  Thus,

the hour hand should be 1/4 of the 

distance between the 3 and 4.

1/4 of the 30 degree space is 

7.5 degrees.

The minute hand will be straight on the

3 and the hour hand 7.5 degrees past it.

 

7.5 degrees