Answer:
The length of the arc is [tex]8\pi\ ft[/tex]
Step-by-step explanation:
we know that
The measure of the arc shown in brown is equal to
[tex]180\°-60\°=120\°[/tex] -----> by central angle
Remember that
The length of the arc of the complete circle (360 degrees) is equal to the circumference
[tex]C=\pi D[/tex]
we have
[tex]D=24\ ft[/tex]
substitute
[tex]C=\pi (24)=24 \pi\ ft[/tex]
so
by proportion
Find the length of the arc for a measure of [tex]120\°[/tex]
[tex]\frac{24\pi }{360} \frac{ft}{degrees} =\frac{x }{120} \frac{ft}{degrees}\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft[/tex]
