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What's the angle between the minute hand and the hour hand (measuring clockwise) at 4:07:19 AM?

 May 6, 2015

Best Answer 

 #1
avatar+128577 
+10

 

 

The hour hand moves 1/12 x 360°  in every hour = 30° every hour or 30/3600 = 1/120°  every second.....at 4AM it had advanced 120° since midnight.

 

But, since 7 minutes and 19 seconds = 439  seconds....it has advanced an additional 439/120 =  3.6583°  since 4AM .....so it has advanced 123.8583°  since midnight

 

The minute hand advances 360° every hour = 6°  every minute. So, in 7 minutes it has advanced 42° since the top of the hour plus another 19/60 x 6°  = 1.9°....so it has advanced 43.9°  since 4AM

 

So...the angle between the hands is  [ 123.8583 - 43.9  ]°  = about 79.7583°  {I assume you might want the negative of this iif we're measuring clockwise  ???}

 

  

 May 6, 2015
 #1
avatar+128577 
+10
Best Answer

 

 

The hour hand moves 1/12 x 360°  in every hour = 30° every hour or 30/3600 = 1/120°  every second.....at 4AM it had advanced 120° since midnight.

 

But, since 7 minutes and 19 seconds = 439  seconds....it has advanced an additional 439/120 =  3.6583°  since 4AM .....so it has advanced 123.8583°  since midnight

 

The minute hand advances 360° every hour = 6°  every minute. So, in 7 minutes it has advanced 42° since the top of the hour plus another 19/60 x 6°  = 1.9°....so it has advanced 43.9°  since 4AM

 

So...the angle between the hands is  [ 123.8583 - 43.9  ]°  = about 79.7583°  {I assume you might want the negative of this iif we're measuring clockwise  ???}

 

  

CPhill May 6, 2015

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