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

The arc length is 185.39 meters.

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 =(8)/(5)\pi\, rad`, the arc length, measured in meters, is:

`\Delta s = (8)/(5)\pi\cdot (36.9\,m)`

`\Delta s = (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.