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December 31st, 2012, 07:36 AM   #1
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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.
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December 31st, 2012, 07:49 AM   #2
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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.

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December 31st, 2012, 08:07 AM   #3
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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.
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December 31st, 2012, 08:47 AM   #4
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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 pre-calc book? sorry for confusion and thank agentredlum for the answer!
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December 31st, 2012, 08:56 AM   #5
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Re: Ratio of two central angle to the arc lengths of sides

You're welcome. Happy new year and welcome to the forum!

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December 31st, 2012, 09:19 AM   #6
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Re: Ratio of two central angle to the arc lengths of sides

Thank you and happy new year to you too
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