Tiffany B.

asked • 04/23/20

Find the length of an arc that forms a central angle of 100 deg in a circle of radius 7

Please answer & show work!

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Lois C. answered • 04/23/20

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The formula for arc length is S = r θ where r is the radius and θ is the angle measure in radians. Since the angle is given in degrees, we need to first switch the angle measure to radians. We will do this by multiplying the given angle by the conversion factor of π radians/180 degrees. So it looks like this:


100 degrees x π radians/180 degrees. This simplifies to 5π/9 radians. Now we insert this into the formula: S = 5π/9 ⋅ 7 or 35π/9 units.

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Lois C.

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I checked the other answer that was also provided to this question. The set-up for the problem is correct ( it is simply an alternate way of doing this problem) but for the answer, the decimal point should be positioned as 12.2173, approximately the same value as 35pi/9.
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04/26/20

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