SOLUTION: 2 sectors of the same circle have sector angles 35 degrees and 105 degrees the arc length of the smaller sector is 17 cm. what is the arc length of the larger sector? Can you p

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Question 855336: 2 sectors of the same circle have sector angles 35 degrees and 105 degrees the arc length of the smaller sector is 17 cm. what is the arc length of the larger sector?
Can you please help me out? Thanks so much in advance :)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2 sectors of the same circle have sector angles 35 degrees and 105 degrees the arc length of the smaller sector is 17 cm. what is the arc length of the larger sector?
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arc length = r*theta, where theta is measured in radians
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Smaller sector DATA:
35 degrees = 35(pi/180) = (7/36)pi
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Equation:
17 cm = r*(7/36)pi
r = (36*17)/(7pi)
radius = 27.83 cm
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Larger sector DATA:
r = 27.83 cm
theta = 105 deg = 105(pi/180) = (21pi/36) = 7pi/12
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arc length = r*theta = 27.83*(7pi/12) = 51 cm
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You can get the same answer using a proportion::
arclength/angle = arclength/angle
arclength = 105(17/35)
arclength = 51 cm
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Cheers,
Stan H.
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