Question

Find the length of the arc shown in brown. Leave your answer in terms of pi.

Answer 1

Answer:

The length of the arc is $8\pi\ ft$  

Step-by-step explanation:

we know that

The measure of the arc shown in brown is equal to

$180\°-60\°=120\°$ -----> by central angle

Remember that

The length of the arc of the complete circle (360 degrees) is equal to the circumference

$C=\pi D$

we have

$D=24\ ft$

substitute

$C=\pi (24)=24 \pi\ ft$

so

by proportion

Find the length of the arc for a measure of $120\°$

$\frac{24\pi }{360} \frac{ft}{degrees} =\frac{x }{120} \frac{ft}{degrees}\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft$