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# Find the length of an arc on a circle of radius 8 corresponding to an angle of (90/π)∘.

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Find the length of an arc on a circle of radius 8 corresponding to an angle of (90/π)∘

I keep getting the answer of 229.12 but it asks me to enter it as a fraction

Nov 5, 2019

#1
+108629
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Find the length of an arc on a circle of radius 8 corresponding to an angle of (90/π)∘

I keep getting the answer of 229.12 but it asks me to enter it as a fraction

When you get answers Roxettna you should learn to look at whether that answer is reasonable.

Here you have a circle of radius 8 so the circumference is 2*pi*8 which is about 50units.

pi is just a bit more than 3 so 90/pi is about 30degrees.  Which is only a little bit of a circle so the answer must be way less than 50.

Now  the circumference of a circle is    2*pi* r

There are 360 degrees in a revolution.

so

you have     90/pi  divided by 360   of the circle

So

$$Arc\; length = \frac{\frac{90}{\pi}}{360}*2\pi r\\ Arc\; length = (\frac{90}{\pi}\div 360)*2\pi r\\ Arc\; length = (\frac{90}{\pi}\times \frac{1}{360})*2\pi r\\ Arc\; length = \frac{1}{4\pi}*2\pi r\\$$

You should be able to finish it from there. Don't forget that r is 8 units

Nov 5, 2019
#2
+136
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I finally got it. The answer is 4/1. Turns out I was multiplying the wrong numbers in the wrong mode :D Thank you so much for being so thorough!!!

Roxettna  Nov 5, 2019