
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 19th, 2012, 02:48 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, 02:56 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, 03:10 AM  #3 
Senior Member Joined: Mar 2012 Posts: 118 Thanks: 0  Re: measure smaller angle 
December 19th, 2012, 03:13 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, 05:21 AM  #5 
Senior Member Joined: Mar 2012 Posts: 118 Thanks: 0  Re: measure smaller angle
168.5 deg

December 19th, 2012, 09:04 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,319 Thanks: 936  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, 09:16 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  Re: measure smaller angle
28 * 6 = 168.

December 19th, 2012, 09:37 AM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,319 Thanks: 936  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, 09:38 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  Re: measure smaller angle
Ah, yes. Missed that . . . darn!

December 19th, 2012, 10:32 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 19,723 Thanks: 1807 
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.


Tags 
angle, measure, smaller 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculating angle sin and sin angle without any functions.  Gyiove  Algebra  1  February 26th, 2014 04:57 PM 
Surface of a ball built up from smaller balls  Chemist@  Algebra  2  September 30th, 2013 06:17 AM 
Mandelbrot asked distance around lake its smaller at night  BenFRayfield  Physics  0  August 24th, 2013 03:10 PM 
The angle between two curves is the angle between  kingkos  Algebra  2  December 7th, 2012 05:34 PM 
how to make the PDF file smaller  Latex  yaron  LaTex Help  3  June 20th, 2010 02:29 PM 