Question

If the arc length shown is 7.5 feet, find r to the nearest hundredth of a foot.

Answer 1

so i think i can solve this, i just need somebody to double check this for me

Answer 2

x/2 π r = y/360

Answer 3

x = 7.5 i think

Answer 4

The angle is in degree measure.... how troublesome :D

Answer 5

@hero this one doesn't give me the r value, how can i solve without that?

Answer 6

r is what you're supposed to find.

Answer 7

yes so its different than the other ones i have posted

Answer 8

hmm i'm confused

Answer 9

Well, given that your angle is (inconveniently) in degree measure, use this formula for arclength s...
\[s = \frac{\theta}{360^o}2\pi r\]
Where theta is the angle measure in degrees

Answer 10

ok i see

Answer 11

You already know that s = 7.5, so go all algebra-like on it or somethin'
:D

Answer 12

y = 45
x/(2 π r) = 45/360

Answer 13

what does y represent here @hero

Answer 14

arc measure

Answer 15

oh ok

Answer 16

You should have written it in your notes

Answer 17

sorry just got confused for a moment

Answer 18

so i am trying to solve for r, but i need to solve for x first right?

Answer 19

x = arc length which is already given

Answer 20

You have to isolate r

Answer 21

And it won't be easy

Answer 22

would you mind explaining how to isolate r?

Answer 23

\[\frac{x}{2 \pi r} = \frac{y}{360}\]
Multiply both sides by r; divide both sides by y
\[\frac{x}{2\pi y} = \frac{r}{360}\]

Mulitply both sides by 360

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

Answer 24

and what does x equal again?

Answer 25

i know y=45 but i forgot x

Answer 26

From there, input all the given values

x = 7.5
y = 45

\[\frac{360(7.5)}{2 \pi(45)} = r\]

Answer 27

ohh thats right

Answer 28

let me see if i can figure it out from there

Answer 29

r=9.55?

Answer 30

:)

Answer 31

Yes, you got it

Answer 32

yayy, thanks for setting it up for me. i actually understood this one!!

Answer 33

9.55 wouldn't be in degrees would it? is there a specific unit i should use?

Answer 34

You only understand it if you can do it without my help

Answer 35

Like completely on your own. I think you should try doing these first, then asking us to verify your answers.

Answer 36

yes, well i could go back and rework this one because you showed me. the other ones i didn't understand at first but this one was more clear

Answer 37

at first i had no clue how to solve it

Answer 38

well thanks again @hero :) i really appreciate it, i have a few more of these to solve and i'll try to do the rest on my own :)