SOLUTION: How do you find the measure of the central angle if the arc length is 20.21 and the circumference is 40.44?

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Question 330651: How do you find the measure of the central angle if the arc length is 20.21 and the circumference is 40.44?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
a complete distance around the circle is the circumference = theta*r or 2*pi*r
representing an arc around the circle. Thetha is the angle in raidants.
therefore the distance of an arc S= Thetha * r
given S=20.21 and the circumference = 40.44
r=Circumference/(2Pi) = 20.22/Pi
Since S=thetha * r solve for Thetha (the central angle in radiants)
Theta = S/r = 20.21/(20.22/Pi) = Pi*(20.21/20.22) = 0.9995*Pi in radiants
or Theta = 0.9995*Pi * (180/Pi) = 179.9 degrees
Theta = S/r = 20.21/(4.4