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Shortly after 10 'o clock, the hands of a clock made a 90 degree angle. What's the time?

 Jun 16, 2021
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At 10:00 the hour hand is at 300 degrees   .....  it moves 1/2 degree per minute

    so the angle it forms with the 12 : oo position is

       360 - 300 - 1/2 x

     the minute hand moves 6 degrees per minute

 

     the angle it forms with 12:00   is      6 x

 

summed they = 90 degrees

 

360-300-1/2 x     +     6x     = 90

60 + 5.5 x = 90

5.5x  = 30

x = 5.45 minutes   ( 5 min 27 sec)                       so at   10:05:27   the hands form a 90 degree angle

 Jun 16, 2021

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