Question

In a circle with a diameter of 25.2 ft, an arc is intercepted by a central angle of 168º.

What is the arc length?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

Answer 1

`36.93\ ft`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=\pi D`

we have

`D=25.2\ ft`

substitute

`C=25.2\pi\ ft`

step 2

we know that

The circumference of a circle subtends a central angle of 360 degrees

so

using proportion

Find out the arc length by a central angle of 168 degrees

`(25.2\pi)/(360)=(x)/(168)\\\\x=25.2\pi*168/360\\\\x=(25.2*3.14)*168/360\\\\x=36.93\ ft`