Problem 1107

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

 

Solution:-

 

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 of θ radians subtends an arc whose length s is

s = r θ

the value of r in the formula is 75 meters.

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

s(arc length) = 75 meters * {1}{15} radian

= 3 meters

 

 

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