Question

Express the required measurement in exact form.

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

help me please

Answer 1

arc length =4pi
circle circumference =20pi {circumference of circle=2pi times radius}
therefore 1/5 of the circle circumference is covered by the arc .
therefore 360/5 =72 deg.

Answer 2

sure. way two
radian measure of angle is arc length divided by radius. in your case \[\frac{4\pi}{10}=\frac{2\pi}{5}\] convert to degrees via
\[\frac{180}{\pi}\times \frac{2\pi}{5}=72\]