Question 1022129
the hour hand of the clock moves 360 degrees in 12 hours.


the number of degrees the hour hand moves per hour is therefore 360 / 12 = 30 degrees.


the hour hand of the clock moves 360 degrees in 12 *60 = 720 minutes.


the number of degrees the hour hand moves per minute is therefore 360 / 720 = 1/2 degrees.


so the hour hand moves 1/2 degree per minute.


the minute hand moves 360 degrees in 60 minutes.


the number of degrees the minute hand moves per minute is therefore 360 / 60 = 6 degrees.


at 5:44, the number of minutes the hour hand has moved is 5 * 60 + 44 = 344 minutes.


at half a degree per minute, the hour hand has moved .5 * 344 = 172 degrees.


at 5:44, the number of minutes the minute hand has moved is 44 minutes.


at 6 degrees per minute, the minute hand has moved 6 * 44 = 264 degrees.


the angle between the minute hand and the hour hand is therefore 264 degrees minus 172 degrees = 92 degrees.


since that angle is less than 180 degrees, it has to be the smaller angle between the hour hand the the minute hand.