Question

Item 4 In a circle with a radius of 36.9 m, an arc is intercepted by a central angle of 8π 5 radians. What is the arc length? Use 3.14 for π and round your final answer to the nearest hundredth.

Answer 1

Answer:

The arc length is 185.39 meters.

Step-by-step explanation:

The arc length is calculated by the following expression:

$\Delta s = \Delta \theta \cdot r$

Where:

$r$ - Radius, measured in meters.

$\Delta \theta$ - Central angle, measured in radians.

If $r = 36.9\,m$ and $\Delta \theta =\frac{8}{5}\pi\, rad$, the arc length, measured in meters, is:

$\Delta s = \frac{8}{5}\pi\cdot (36.9\,m)$

$\Delta s = \frac{8}{5}\cdot (3.14)\cdot (36.9\,m)$

$\Delta s \approx 185.386\,m$

$\Delta s \approx 185.39\,m$

The arc length is 185.39 meters.