# How would you find the length of the arc on a circle with a radius of 20 m intercepted by a central angle of 138°?

Nov 15, 2015

Find the circumference of the circle, then ...

#### Explanation:

Circumference $= 2 \pi r = 2 \pi \left(20\right) = 40 \pi$ meters

Arc Length $= \frac{c e n t r a l \angle}{{360}^{o}} \times \left(C i r c u m f e r e n c e\right) = \frac{138}{360} \times 40 \pi$

$= \frac{46}{3} \pi \approx 48.2$ meters

hope that helps

Nov 15, 2015

I found $48.16 m$

#### Explanation:

You can use the fact that the length $s$ of an arc to an angle $\theta$ (in radians) of a circle of radius $r$ is:
$s = r \cdot \theta$
$\theta = {138}^{\circ} = {138}^{\circ} / \left({180}^{\circ}\right) \cdot \pi = 2.408 \text{rad}$
$s = 2.408 \cdot 20 = 48.16 m$