Question

Find the arc length L of a circle with a radius of 6 feet and an arc measure of 120°. Give the answer in terms of π.

Answer 1

@mathmale , @wolf1728

Answer 2

here arc measure of 120 = 120π /180 = 2π/3 radian
hence length of the arc is given by 6* 2π/3= 4π

Answer 3

So it's 4π?

Answer 4

This is one of my three hardest final questions. I've been working on it for literally 8 hours.

Answer 5

length of arc = radius * (arc measure of the angle)

Answer 6

6*120=720

Answer 7

angle shoul be in radians

Answer 8

use 180° = π radians

(by d way the questio is asking to leave the answer in terms of π )

Answer 9

The circumference is proportional to the arc lenth.

Answer 10

\[
\frac{x}{2\pi r } =\frac{120^\circ}{360^{\circ}}
\]

Answer 11

Do I cross multiply?

Answer 12

Nah, just multiply by \(2\pi r\) and simplify.

Answer 13

Multiply what by 2πr? (it's been a long day sorry)

Answer 14

Both sides.

Answer 15

We are solving for \(x\), which is the arc length.

Answer 16

I'm a bit lost.

Answer 17

So 2πr*x/2πr?

Answer 18

Wait, have you not learned any algebra?

Answer 19

No I have. I've just got a case of the stupid right now.

Answer 20

What you get is: \[
x = \frac{120}{360}\cdot 2\pi r
\]

Answer 21

.33+2π=2.09

Answer 22

* times

Answer 23

in this case, \(r\) is 4

Answer 24

How'd you get 4?

Answer 25

I mean 6

Answer 26

Lol, how'd you get 6?

Answer 27

circle with a radius of 6 feet

Answer 28

Oh wait yes.

Answer 29

So my answer is 12.5?

Answer 30

Exact answer is \(4\pi\), but it evaluates to about 12.57

Answer 31

Okay awesome. Thank you so much!