Question

The central angle of an arc measures 12°. The radius of its circle is 30 inches. What is the length of the arc to the nearest quarter inch

Answer 1

1 in

6 1/4 in


37 1/2 in


94 1/4 in

Answer 2

@Owlcoffee

Answer 3

A central angle has the quality that is is equal the arc it intersects.
The definition of a central angle is that it's an angle, composed of two radiuses and the center of the circumference and is equal the arc it intersects.

\[<O=arc.AB\]
now, what we have to do, knowing that, is calculate the perimeter of the circle and sustract 12 from it.

Answer 4

The perimeter of the circle ?

Answer 5

@Owlcoffee

Answer 6

yes, it's calculated:
\[P_\circ =2 \pi r\]

Answer 7

Does it specify the what arc they want you to calculate?

Answer 8

You find the perimeter but you don't subtract 12 from it.

You find the perimeter and then multiply that perimeter (aka circumference) by 12/360

Answer 9

Yes, I was doubting that method would work out.
thanks @jim_thompson5910

Answer 10

30

Answer 11

@Owlcoffee

Answer 12

or 94.2?

Answer 13

@jim_thompson5910

Answer 14

@GodlyMaths

Answer 15

what circumference did you get?

Answer 16

6.28

Answer 17

use C = 2*pi*r where r = 30 in this case

Answer 18

188.4

Answer 19

now multiply that by 12/360

Answer 20

you are doing this because the arc is 12/360 of the circle's full perimeter

Answer 21

okay so i multiply 188.4 x 12 x 360 ? or 188.4 x 12/360?

Answer 22

188.4 x 12/360

Answer 23

6.28

Answer 24

round that to the nearest quarter inch

Answer 25

6 1/4?

Answer 26

good