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

Answer:

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

Step-by-step explanation:

We can use the formula

$2\pi \times r( \frac{x}{360} )$

to find the arc length where r is the radius.

and x is the arc measure.

Plug it in for the numbers

$2\pi \times 5( \frac{60}{360} )$

Multiply 2 pi times 5=10 pi

$10\pi( \frac{60}{360} )$

Simplify 60/360 to 1/6

$10\pi \times \frac{1}{6} = \frac{10\pi}{6}$

Reduce it to

$\frac{5\pi}{3}$