Problem 1109

Find the length s of the arc of a circle of radius 85 centimeters subtended by the central angle 36°.




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.

Arc Length

For a circle of radius r, a central angle θ radians subtends an arc whose length s is

s = r θ

Convert angle in degrees to radians.

1° = \frac{\pi}{180} radian

36° = 36 *\frac{\pi}{180} radian

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

s(arc length) = rθ

= 85 centimeters* \frac{\pi}{5}

=17π centimeters

\approx 53.407 centimeters



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