Problem 659

Find the length s of the circle of radius 75 meters subtended by the center angle \frac{1}{25}radian.


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


The value of r in the formula is 75 meters.

The value of \theta in the formula is \frac{1}{25} radian.

S(arc length) = 75 meters*\frac{1}{25}radian

= 3 meters

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