SOLUTION: What is the number of degrees in the smaller angle formed by the hands of a clock at 5:44?

Question 1022129: What is the number of degrees in the smaller angle formed by the hands of a clock at 5:44?
Found 2 solutions by Theo, Edwin McCravy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Here's another way to do it. Think of the clock face being marked 0� at 12:00PM, 90� at 3:00, 180� at 6:00PM and 270� at 9:00PM. Since there are 60 minute markers around the clock face they are 360�/12 or 6� apart. The numerals are 30� apart. Then at 5:00PM the minute hand is at 0� and the hour hand is at 150�, 30� less than 6:00PM. At 5:44PM the minute hand has turned through 44x6� or 264� since 5:00PM, so the minute hand is at 264�. But the hour hand has only turned 1/12th that many degrees or only 1/12th of 264� or 22�, so at 5:44PM it's at 150�+22� or at 172�. So the angle between them is 264�-172� or 92�. Edwin

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