Puzzle – Hands on a Clock
June 6, 2010 – 12:26 amFor a given time, what will be the angle between the hour and minute hands on a clock?
This is rather a long winded way of solving this, so please let me know if you have something shorter.
The angle of the minute hand (from 12 O’clock):
= (minutes / 60) * 360
The angle of the hour hand (from 12 O’clock) is the angle of the hour plus an adjustment for the minutes:
= (hours / 12) * 360 + (minutes / 60) * (1 / 12) * 360
So to get the angle between them we subract the two, and get:
= (hours / 12) * 360 + (minutes / 60) * (1 / 12) * 360 – (minutes / 60) * 360
= (hours * 30) + minutes * .5 – minutes * 6
= hours * 30 – minutes * 5.5
Any angle over 180 we can subtract from 360 to get the shortest angle between them.