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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 near

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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
#1
+7489
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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 .

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

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

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

$$\large \alpha=21.49\ deg$$

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

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asinus  Apr 4, 2017
#2
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THANKS

Guest Apr 4, 2017
#3
+89953
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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°

CPhill  Apr 4, 2017
#4
+7489
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Thanks, Guest and Chris, for your thanks.
I like the method of Chris too.

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asinus  Apr 4, 2017