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December 31st, 2012, 07:36 AM  #1 
Newbie Joined: Dec 2012 Posts: 3 Thanks: 0  Ratio of two central angle to the arc lengths of sides
My math books states the follow. Inside the circle, two central angle are formed. One angle is theta with r radius and s arc length. And another angle is Theta1 with s1 arc length and it says that the ratio of theta to theta1 is equal to s to s1...can you prove me how is that equal? See the picture below to visualize.

December 31st, 2012, 07:49 AM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Ratio of two central angle to the arc lengths of sides
From the definition of arc length. using the definition and your diagram Now divide. 
December 31st, 2012, 08:07 AM  #3 
Member Joined: Oct 2012 Posts: 56 Thanks: 0  Re: Ratio of two central angle to the arc lengths of sides
I think I know part of that. I'm not sure about the rest. 
December 31st, 2012, 08:47 AM  #4 
Newbie Joined: Dec 2012 Posts: 3 Thanks: 0  Re: Ratio of two central angle to the arc lengths of sides
Well, I am not asking you to find the measurement. I am asking why the rations of thetas to their respective side lengths are equals as stated by my precalc book? sorry for confusion and thank agentredlum for the answer!

December 31st, 2012, 08:56 AM  #5 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Ratio of two central angle to the arc lengths of sides
You're welcome. Happy new year and welcome to the forum! 
December 31st, 2012, 09:19 AM  #6 
Newbie Joined: Dec 2012 Posts: 3 Thanks: 0  Re: Ratio of two central angle to the arc lengths of sides
Thank you and happy new year to you too


Tags 
angle, arc, central, lengths, ratio, sides 
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