Question

A central angle in a circle with a radius of 3 cm intercepts an arc with a length of 6 cm what is the measure of the central angle

Answer 1

`114.59\°`

Explanation:

we know that

The circumference of a circle is equal to

`C=2\pi r`

In this problem we have

`r=3\ cm`

substitute

`C=2\pi (3)=6 \pi\ cm`

Remember that

`360\°` subtends the arc length of the complete circle

so

by proportion

Find the measure of the central angle for an arc length of
`6\ cm`

`(360)/(6\pi ) (degrees)/(cm) =(x)/(6) (degrees)/(cm) \\ \\x=6*360/(6\pi )\\\\ x=114.59\°`