Question

The arc corresponding to a central angle of 125 degrees in a circle of radius 10 feet measures _____ feet. Round your answer to two decimal places.

Answer 1

$\frac{Angle}{360}$ x $2 \pi r$

$\frac{125}{360}$ x $2 \pi (10)$ = $21.82$

Answer: The Arc measures $21.82 feet$

Answer 2

Answer:

$21.82\ ft$

Step-by-step explanation:

we know that

The circumference of a complete circle is equal to

$C=2\pi r$

In this problem we have

$r=10\ ft$

substitute

$C=2\pi (10)=20 \pi\ ft$

Remember that

An angle of $360\°$ subtends the arc length of a complete circle

so

by proportion

Find the arc length for an angle of $125\°$

$\frac{20 \pi}{360}\frac{feet}{degrees}=\frac{x}{125}\frac{feet}{degrees}\\ \\x=125*(20\pi )/360\\ \\x=21.82\ ft$