So this problem dropped in my mail today
Given a clock time in hh:mm format, determine, to the nearest degree, the angle between the hour and the minute hands.
Hours
From a basic understanding of a clock we can say that every 3 hours is 90 degrees.Therefore every hour is 30 degrees.
To put this into an equation, "on the hour", the hour hand is at -
h * 30 degrees
Example: At 4 o'clock the hour hand is at 120 degrees
We have already established above that the hour hand moves 30 degree in an hour.
An hour has 60 minutes. Therefore every minute, the hour hand should move 0.5 degrees.
Example-
At 4:15 the hour hand should have moved 7.5 degree from the 4 o'clock position.
120 + 7.5 = 127.5 degrees
Minutes
Converting minutes to angles is simple
There are 60 minutes. There are 360 degrees. Each minute is 6 degrees
Example - At 15 minutes past the hour the minute hand is at 90 degrees
15 * 6 = 90
Putting the two together
- Find the angle of the hour hand given the information above
- Find the angle of the minute hand given the information above
- Subtract the two angles taking into account whether we are measuring from hour to minute, or minute to hour.
