Question

For a circle with a radius of 6 feet, what is the measurement of the central angle (in degrees) that intercepts an arc with a length of

9π
2
feet?

Answer 1

135 degrees

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=6\ ft`

substitute

`C=2\pi (6)`

`C=12\pi\ ft`

step 2

Remember that the circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the measurement of the central angle (in degrees) that intercepts an arc with a length of 9π/2 ft

`(12\pi)/(360^o)=((9\pi/2))/(x)\\\\x=360(9\pi/2)/12\pi\\\\x=135^o`