How would you find the length of the arc on a circle with a radius of 15 cm intercepted by a central angle of 60°?

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Answer 1 · 2015-12-31T23:07:02

$5 π$ $5pi$ cm

First, we'll need to convert degrees into radians. For that, we need to simply multiply the value with $\frac{π}{180^{o}}$ $pi/180^o$

So $60^{o}$ $60^o$ , in radians,

$= 60^{o} \cdot \frac{π}{180^{o}}$ $=60^o * pi/180^o$

$= \frac{π}{3}$ $=pi/3$ radians.

Now, the formula for the length of an arc is,

$l = r θ$ $l=rtheta$

where,
$l$ $l$ is the length of the arc
$r$ $r$ is the radius of the circle
$θ$ $theta$ is the angle subtended by the circle in radians

Substituting given values in our formula,

$l = 15 \cdot \frac{π}{3}$ $l=15*pi/3$

$l = 5 π$ $l=5pi$ cm