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On a circle of radius 8 feet, give the degree measure of the angle that would subtend an arc of length 3 feet. Round your answer to the nearest hundredth, or two decimal places

Guest Apr 4, 2017
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4+0 Answers

 #1
avatar+7155 
+1

On a circle of radius r= 8 feet, give the degree measure of the angle \(\alpha\) that would subtend an arc of length 3 feet. Round your answer to the nearest hundredth, or two decimal places .

 

\(\large arc=2\pi r\cdot \frac{\alpha}{360deg}\)

 

\(\large \alpha=\frac{arc \cdot 360deg }{2\cdot \pi\cdot r}\)

 

\(\large \alpha=\frac{3ft \cdot 360deg }{2\cdot \pi\cdot 8ft}\)

 

\(\large \alpha=21.49\ deg\)

 

\(\large The \ arc \ of \ the \ length \ 3 feet \ is \ formed \ by \ an \ angle \ of \ 21.49\ deg.\)

 

laugh  !

asinus  Apr 4, 2017
 #2
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+1

THANKS

Guest Apr 4, 2017
 #3
avatar+79716 
+2

Thanks asinus....here's another way

 

s  = r * theta in radians  .......where s is the arc length and r is the radius...so we have  

 

3  = 8 * theta

 

3/8  = theta  ......  convert to degrees

 

3/8  * 180 / pi   ≈ 21.486° 

 

 

cool cool cool

CPhill  Apr 4, 2017
 #4
avatar+7155 
+1

Thanks, Guest and Chris, for your thanks.
I like the method of Chris too.

smiley  !

asinus  Apr 4, 2017

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