Question

20 POINTS * A circle has a radius of 6. An arc in this circle has a central angle of 48°

What is the length of the arc?
Either enter an exact answer in terms of it or use 3.14 for it and enter your answer as a decimal.

Answer 1

`(8\pi)/(5)`

Explanation:

Since this is a degree we going to use the arc length formula

`2\pi *( r)( (x)/(360))`

where x is the central angle measure and r is the radius.

The radius is 6 and the central angle is 48 so let plug that in the formula

`2\pi * (6)( (48)/(360) )`

Multiply 2 pi by 6

`12\pi * ( (48)/(360) )`

`12\pi * (4)/(30)`

`(12\pi)/(1) * (4)/(30) = (48\pi)/(30)`

`(8\pi)/(5)`