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December 19th, 2012, 03:48 AM  #1 
Senior Member Joined: Mar 2012 Posts: 118 Thanks: 0  measure smaller angle
What is the measure of the smaller angle formed by the minute and hour hands of a clock at 3:47 ?

December 19th, 2012, 03:56 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: measure smaller angle
The smaller angle is <= 180 degrees. From the positions of the hands at 12.00 PM, the hour hand turned (3 * 60 + 47)/(60 * 12) * 360 degrees clockwise. The minute hand has turned 47/60 * 360 (mod 360) degrees clockwise. What will the angle be? 
December 19th, 2012, 04:10 AM  #3 
Senior Member Joined: Mar 2012 Posts: 118 Thanks: 0  Re: measure smaller angle 
December 19th, 2012, 04:13 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: measure smaller angle
Yes, how large is the angle?

December 19th, 2012, 06:21 AM  #5 
Senior Member Joined: Mar 2012 Posts: 118 Thanks: 0  Re: measure smaller angle
168.5 deg

December 19th, 2012, 10:04 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,796 Thanks: 970  Re: measure smaller angle
6.5 : hour hand from 4 60 : 4 to 6 90 : 6 to 9 12 : minute hand past 9 ==================== 168.5 : total 
December 19th, 2012, 10:16 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,900 Thanks: 1093 Math Focus: Elementary mathematics and beyond  Re: measure smaller angle
28 * 6 = 168.

December 19th, 2012, 10:37 AM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,796 Thanks: 970  Re: measure smaller angle Quote:
47 / 60 * 30 = 23.5 ; 30  23.5 = 6.5 AD: "If your clock don't tick, tock to us!"  
December 19th, 2012, 10:38 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,900 Thanks: 1093 Math Focus: Elementary mathematics and beyond  Re: measure smaller angle
Ah, yes. Missed that . . . darn!

December 19th, 2012, 11:32 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,101 Thanks: 1905 
Was the wobbly blue line in the diagram part of the question or a guess at the intended angle? It's arguable that the larger angle is the obtuse angle and the smaller angle is the unmarked acute angle (which is 11.5°), as the unmarked reflex angle can be ignored. By the way, I doubt that any real clock has been made that looks like the illustration provided, as the minute hand should be on top.


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