Question

can somebody please explain how i should solve this? i'd really appreciate it :)

Find the indicated arc length.

The arc corresponding to a central angle of 35° in a circle of radius 10 feet

Answer 1

Hint: x = arc length

\[\frac{x}{2\pi r} = \frac{35}{360}\]

Answer 2

r is the radius correct?

Answer 3

Yes

Answer 4

In general

\[\frac{\text{arc length}}{\text{circumference}} = \frac{\text{arc measure}}{\text{circle measure}}\]

Answer 5

oh i see

Answer 6

so from x/2πr=35/360 how do i continue to solve it

Answer 7

Isolate x

Answer 8

of course r = 10 so input that then isolate x

Answer 9

It's not really difficult. If you know how to solve proportions, you should be able to solve this.

Answer 10

ok, so what do i use for pi

Answer 11

3.14?

Answer 12

3.14 or you can just leave it as \(\pi\)

Answer 13

It's best to just leave it as \(\pi\)

Answer 14

Isolate x then reduce the fraction.

Answer 15

so x/62.83=.097?

Answer 16

does that work?

Answer 17

Yes, but it is an approximation, so it's not exact

Answer 18

First solve the exact, then find the approximate

Answer 19

how do i solve the exact

Answer 20

any time you solve a problem, you should post the exact answer, and then after that, post the approximate answer

Answer 21

i'm not exactly sure how to find the exact, just the approximate :(

Answer 22

\(\large\frac{x}{2 \pi (10)} = \frac{35}{360}\)

\(\large\frac{x}{20\pi} = \frac{35}{360}\)

\(\large x = \frac{35}{360} \dot\ 20\pi\)

\(\large x = \frac{35 \dot\ 20\pi}{360}\)

\(\large x = \frac{35 \pi}{18}\)

\(x \approx 6.11\)

Answer 23

That's how you should solve all math problems that have approximate answers. Post the exact answer first in reduced form. Then post the approximate result.

Answer 24

oh i see

Answer 25

it makes much more sense now

Answer 26

so the arc would be approximately 6.11 degrees?

Answer 27

ya

Answer 28

thanks so much you're so great at this stuff

Answer 29

It's not difficult stuff

Answer 30

haha well for me it is, but i dont understand it when i read it from a book, this kind of explanation helps me a lot more

Answer 31

can you please help explain the one i just posted? its the same type of problem, i'd like to get practice with more than one just to be sure that i understand the topic

Answer 32

Actually, there's a three fraction ratio for this that shows the relationship between length, measure, and area of a circle

\[\frac{\text{arc length}}{\text{circumference}} = \frac{\text{arc measure}}{\text{circle measure}} = \frac{\text{area of sector}}{\text{area of circle}}\]

Answer 33

In the simplest manner:

\[\frac{x}{2 \pi r} = \frac{y}{360} = \frac{z}{\pi r^2}\]

x = arc length
y = arc measure
z = area of sector

Answer 34

the numerator represents a portion of the circle. the demoninator represents the whole circle.

Answer 35

ohh ok i see

Answer 36

thanks again :)