Clock angle problem
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A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute.
Equation for the angle of the hour hand
- θ is the angle in degrees of the hand measured clockwise from the 12
- MΣ is the minutes past 12 o'clock.
- H is the hour.
- M is the minutes past the hour.
Equation for the angle of the minute hand
- θ is the angle in degrees of the hand measured clockwise from the 12 o'clock position.
- M is the minute.
The time is 5:24. The angle in degrees of the hour hand is:
The angle in degrees of the minute hand is:
Equation for the angle between the hands
The angle between the hands can be found using the following formula:
- H is the hour
- M is the minute
If the angle is greater than 180 degrees then subtract it from 360 degrees
The time is 2:20.
When are the hour and minute hands of a clock superimposed?
The hour and minute hands are superimposed only when their angle is the same.
H is an integer in the range 0–11. This gives times of: 0:00, 1:05.45, 2:10.90, 3:16.36, 4:21.81, 5:27.27. 6:32.72, 7:38.18, 8:43.63, 9:49.09, 10:54.54, and 12:00. (0.45 minutes are exactly 27.27 seconds.)
- http://www.ldlewis.com/hospital_clock/ - extensive clock angle analysis