Problem 661

Find the length s of the arc of a circle of radius 85 centimeters subtended by the center angle 36^{\circ}.


A central angle is an angle whose vertex is at the center of a circle. The rays of a central angle subtend (intersect) an arc on the circle. We have the following theorem.



For a circle of a radius r, a center angle of  \theta radian subtends an arc whose length s is

s = r\theta


Convert angle in degrees to radians.

1^{\circ} = \frac{\pi}{180} radian

36^{\circ}= 36*= \frac{\pi}{180} radian

\approx\frac{\pi}{5} radian


S (arc length)= r\theta

= 85 centimeters.\frac{\pi}{5}radian

= 17\pi centimeters



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