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December 19th, 2012, 02:48 AM   #1
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measure smaller angle

What is the measure of the smaller angle formed by the minute and hour hands of a clock at 3:47 ?
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December 19th, 2012, 02:56 AM   #2
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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?
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December 19th, 2012, 03:10 AM   #3
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Re: measure smaller angle

http://assets.openstudy.com/updates/att ... apture.png


now what is the exact degree
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December 19th, 2012, 03:13 AM   #4
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Re: measure smaller angle

Yes, how large is the angle?
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December 19th, 2012, 05:21 AM   #5
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Re: measure smaller angle

168.5 deg
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December 19th, 2012, 09:04 AM   #6
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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
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December 19th, 2012, 09:16 AM   #7
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Re: measure smaller angle

28 * 6 = 168.
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December 19th, 2012, 09:37 AM   #8
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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

AD: "If your clock don't tick, tock to us!"
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December 19th, 2012, 09:38 AM   #9
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Re: measure smaller angle

Ah, yes. Missed that . . . darn!
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December 19th, 2012, 10:32 AM   #10
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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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