Answer to Puzzle #5

How many degrees (if any) are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?  

I worked this one out for myself too so it clearly isn't that hard either...

First consider the picture below:-

Clearly there is an angle between the hour and minute hand other than zero. This comes from the fact that the hour hand doesn't stay still whilst the minute hand is catching up. So let us consider the angles clockwise from 12 o'clock so.

12 o'clock = 0°
1 o'clock = 30°
2 o'clock = 60°
3 o'clock = 90°
 4 o'clock = 120°

The simplest way to think of this is that clearly each hour is made up of 30° and that the hour hand will have moved one quarter of an hour past three o'clock. ¼ x 30° = 7.5°

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