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

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) (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
RELATED QUESTIONS
Anyone willing to tackle these two: Please explain process. Bless you.... (answered by Alan3354,lwsshak3)

A circle with circumference 20π has an arc with a 23 degree central angle. What... (answered by Alan3354)

Determine the arc length if the central angle measures 40 degrees and the radius of the... (answered by dkppathak)

The central angle of a minor arc is 40 degrees.The angle subtended by the corresponding... (answered by ikleyn)

Find the measure of the central angle of an arc if its length is 14 pi and the radius is... (answered by josgarithmetic)

If the circumference of a circle is 24, and the angle measure of an arc is 120o, which is (answered by stanbon)

How do you find the radian measure of the central angle of a circle of radius 1 yard that (answered by dabanfield)

Find the degree measure, to the nearest tenth, of the central angle whose intercepted arc (answered by scott8148)

Find the measure of a central angle θ in a circle of radius 5ft if the angle is... (answered by Alan3354)