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 \(L=r\times \theta\)
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
\(1^\circ= \frac{\pi }{180}\) radians
\(57^\circ= 57\times\frac{\pi }{180}\) radians
Substitute in the formula,
\(L=r\times \theta\)
\(L=3\times 57\times\frac{\pi}{180}\)
\(L=57\times\frac{\pi}{60}\)
\(L=0.95\pi\)
\(L=0.95\times 3.14=2.98\)
Therefore, The length of the arc is 2.98 feet.
