Question

Express the required measurement in exact form.

What is the degree measure of an arc 4 pi ft. long in a circle of radius 10 ft.?

Answer 1

Arc is
\[c=r \theta \]
So you have
\[4 \pi= 10 \theta \]
So
\[\theta=\frac{4 \pi}{10}=\frac{2 \pi}{5}\]
In radians

Answer 2

use theta=s/r so angle in radians is 4pi/10=2pi/5 Now angle in degrees is (180/pi)*(2pi/5)=360/5

Answer 3

Meaning 72 degrees

Answer 4

\[\theta=s/r\]
\[\theta=2\pi/5\]
\[\theta=(2\pi/5)(180/\pi)=72 degrees\]