Question

Find the length of arc AC Express your answer in terms of pi AB = 12 AND dEGREE Is 60

Answer 1

where is arc C?

Answer 2

whoops sorry

Answer 3

I mean point C in the circle?

Answer 4

sorry

Answer 5

its okay

Answer 6

Formula for the length of an arc is : Pi times diameter i might be getting my fourmlas mix up

Answer 7

so since the angle given is 60 degrees, we assume the line that you draw will be equal to 180 degrees. To find the angle of arc AC, we subtract 180 - 60 which is 120 degrees. We will be using this later.

In a circle, it holds true that in any points of the circle represent the radius, so to find the radius of the circle given,

\[a=r \theta \] where \[r=a/\theta \] where the value of theta is in radians not degrees

\[r=12/{\Pi/3} \] which is equal to 11.5 feet. We will be using this radius to find the measurement of arc AC.

\[a=r \theta \]

\[a=(11.5)(2\Pi/3)\] which is equal to 24.1 feet.

Therefore, arc AC is equal to approximately 24 feet.

Answer 8

I think they want the answer in terms of PI
radius = 6
circumference (entire circle) = 2*PI*6
circumference for 60 degrees = 1/6
circumference 60 degrees = 2*PI*6 * (1/6)
circumference 60 degrees = 2 * PI

Answer 9

So 2 pi the answer?

Answer 10

Yes, 2 * PI is the answer.