Answer:
[tex]8\:\text{ft}[/tex]
Step-by-step explanation:
The length of the arc is proportional to the degree measure it in encompasses. Since there are 360 degrees in a circle and the arc is 120 degrees, the arc's length will be [tex]\frac{120}{360}=\frac{1}{3}[/tex] of the circle's length (circumference).
The circumference of a circle is given by [tex]2\pi r[/tex], where [tex]r[/tex] is the radius of the circle. Therefore, the circumference of the circle is [tex]2\pi(4)=8\pi[/tex]. As we found earlier, the length of the arc is [tex]\frac{1}{3}[/tex] of this circumference. Therefore, the arc's length is [tex]8\pi\cdot \frac{1}{3}=\frac{8\pi}{3}[/tex].
To the nearest integer, this is [tex]\approx \boxed{8\:\text{ft}}[/tex].
