SOLUTION: A circular arc has length 3 cm, and the radius of the circle is 2 cm. What is the measure of the angle subtended by the arc, in both radians and degrees?

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Question 564119: A circular arc has length 3 cm, and the radius of the circle is 2 cm. What is the measure of the angle subtended by the arc, in both radians and degrees?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A circular arc has length 3 cm, and the radius of the circle is 2 cm. What is the measure of the angle subtended by the arc, in both radians and degrees?
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theta(in radians) = arc length/radius = 3/2
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theta (in degrees) = (3/2)(180/pi) = 270/pi = 85.94 degrees
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Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The circumference is +2%2Api%2A2+=+4%2Api+ cm
The ratio of ( arc in radians ) / ( 2pi ) = ( 3 cm ) / ( 4pi )
+r+%2F+%282%2Api%29+=+3+%2F+%284%2Api%29+
Multiply both sides by +4%2Api+
+2r+=+3+
+r+=+2%2F3+ radians
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I can say:
+%28+2%2F3+%29+%2F+pi+=+d+%2F+180++
Multiply both sides by +180%2Api+
+%282%2F3%29%2A180+=+d%2Api+
+120+=+d%2Api+
+d+=+120%2Fpi+
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The arc is 2/3 radians or 120/pi degrees
check:
+%28+120%2Fpi+%29+%2F+360+=+%282%2F3%29+%2F+%28+2%2Api+%29+
Multiply both sides by +360%2Api+
+120+=+%282%2F3%29%2A180+
+120+=+120+
OK