Question 1127681: Suppose an angle has a measure of 110 degrees.
a. If a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is ______________ times as long as 1/360th of the circumference of the circle.
b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.07 cm long. What is the length of the arc subtended by the angle's rays?
______cm
c. Another circle is centered at the vertex of the angle. The arc subtended by the angle's rays is 44 cm long.
-1/360th of the circumference of the circle is _________ cm long.
-Therefore the circumference of the circle is__________cm.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose an angle has a measure of 110 degrees.
110 degress = (pi/180)110 = 0.61radians
1 degree = (pi/180) = 0.017 radians
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a. If a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.61/0.017 = 34.95 times as long as 1/360th of the circumference of the circle.
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b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.07 cm long. What is the length of the arc subtended by the angle's rays?
34.95*0.07 cm = 2.6465 cm
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c. Another circle is centered at the vertex of the angle. The arc subtended by the angle's rays is 44 cm long.
-1/360th of the circumference of the circle is 44/34.95 = 1.2589 cm long.
-Therefore the circumference of the circle is 360*1.2589 = 453.22 cm.
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Cheers,
Stan H.
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