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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 http://assets.openstudy.com/updates/att ... apture.png now what is the exact degree
 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:
 Originally Posted by greg1313 28 * 6 = 168.
Disagree: hour hand is at 23.5 from 3, so 6.5 from 4:
47 / 60 * 30 = 23.5 ; 30 - 23.5 = 6.5

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 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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