Answer:
The length of the arc is 2.98 feet.
Step-by-step 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 [tex]L=r\times \theta[/tex]
Where L is the arc length, r is the radius and [tex]\theta[/tex] is the angle (in radians)
The radius given is r=3 feet.
The angle subtended is [tex]\theta=57^\circ[/tex]
Convert degree into radians
[tex]1^\circ= \frac{\pi }{180}[/tex] radians
[tex]57^\circ= 57\times\frac{\pi }{180}[/tex] radians
Substitute in the formula,
[tex]L=r\times \theta[/tex]
[tex]L=3\times 57\times\frac{\pi}{180} [/tex]
[tex]L=57\times\frac{\pi}{60}[/tex]
[tex]L=0.95\pi [/tex]
[tex]L=0.95\times 3.14=2.98 [/tex]
Therefore, The length of the arc is 2.98 feet.
