You can put this solution on YOUR website! At what time after 5 o'clock will the hands of the clock be forming 120 degrees?
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Let x = position of the minute hand when this occurs:
:
Convert the hr hand to degrees.
360/12 = 30 degrees per hr
The portion of a 5 min interval of the hour hand would be:
x/60*30 = .5x
;
Convert min hand do degrees
360/60 = 6 degrees per minute
Number of degrees by the minute hand would be 6x
:
5 o'clock = 5 * 30 = 150 degrees (added to the hr hand degrees)
:
Min hand position - hr hand position = 120 degrees
6x - (150 + .5x) = 120
6x - 150 - .5x = 120
6x - .5x = 120 + 150
5.5x = 270
x = 270-5.5
x = 49.1 min
:
The time when the hands form a 120 degree angle would be 5:49.1
