Question

Circle O has a radius of 5 centimeters and central angle AOB with a measure of 60°. Describe in complete sentences how to find the length, in terms of a radian measure, of AB.

Answer 1

We can use the formula for finding arc length given ccx central angle and radius.(insert formula below) We then substitute 5 in for r and and 60 for x. We multiply 2 pi times 5 which gives us 10. We then reduce the fraction of 60/360 to 1/6. We multiply 10 pi by 1/6 and that gives us

10 pi/6 or 5 pi/3

Explanation:

We can use the formula

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

to find the arc length where r is the radius.

and x is the arc measure.

Plug it in for the numbers

`2\pi * 5( (60)/(360) )`

Multiply 2 pi times 5=10 pi

`10\pi( (60)/(360) )`

Simplify 60/360 to 1/6

`10\pi * (1)/(6) = (10\pi)/(6)`

Reduce it to

`(5\pi)/(3)`