Question

For a circle of radius 3 feet, find the arc length s subtended by a central angle of 57 degrees.

Answer 1

s = r π α / 180°
r = 3 ft, α = 57°
s = 3 · π · 57° / 180° = 19/20 π ft = 0.95 π ft ≈ 2.983 ft
Answer: the arc length is 2.983 ft.

Answer 2

The length of the arc is 2.98 feet.

Explanation:

Given : For a circle of radius 3 feet, the arc length s subtended by a central angle of 57 degrees.

To find : The arc length

Solution :

Formula of arc length is
`L=r* \theta`

Where L is the arc length, r is the radius and
`\theta` is the angle (in radians)

The radius given is r=3 feet.

The angle subtended is
`\theta=57^\circ`

Convert degree into radians

`1^\circ= (\pi )/(180)` radians

`57^\circ= 57*(\pi )/(180)` radians

Substitute in the formula,

`L=r* \theta`

`L=3* 57*(\pi)/(180)`

`L=57*(\pi)/(60)`

`L=0.95\pi`

`L=0.95* 3.14=2.98`

Therefore, The length of the arc is 2.98 feet.