Question

i'm lost, can someone please explain?

If the arc length shown is 21.3 inches, find θθ to the nearest hundredth of a radian.

Answer 1

Use the ratios I showed you

Answer 2

which one? sorry can u repost here?

Answer 3

Well, we're not dealing with area, so the only two units that apply are length and measure.

Answer 4

right

Answer 5

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

Plug in r = 12, x = 21.3. solve for y

Answer 6

46.98=y/360

Answer 7

so y would equal 16912.8? for some reason i think i did it wrong :(

Answer 8

Yes, you definitely did something wrong

Answer 9

did you plug in x and r in the right place

Answer 10

i put 21.3/π(12)=y/360

Answer 11

is that right?

Answer 12

@hero

Answer 13

What happened to the 2 in the denominator? You left that out

Answer 14

i put 21.3/(2π(12))=y/360

Answer 15

ooh my fault

Answer 16

Next thing is to isolate y by multiplying both sides by 360

Answer 17

let me solve from there one moment

Answer 18

y=27144 is this right?

Answer 19

ugh did i do something wrong again

Answer 20

Yes, you did something wrong. I don't know what

Answer 21

Do you know how to solve proportions?

Answer 22

not too well

Answer 23

i did 2*pi*12 and got 75.4

Answer 24

and then did 75.4=y/360 which was probably wrong

Answer 25

Of course that's wrong because what did you do with the 21.3 ?

Answer 26

Or
\[s = r \theta \]

s=arc length
r=radius
\[\theta\] = measure of angle

manipulate the formula to isolate \[\theta\]
\[\theta\ = r / s\]

so \[\theta = 21.3/12\]


another way to look at it. Hero is also correct.

Answer 27

@Leemah! , I already knew you were going to post that. I can tell that you were itching to post it the whole time.

Answer 28

right!! how did i forget about that haha so if i remember the 21.3 then i get 401.5=y/360 correct?

Answer 29

Yes, I find it easier.

Answer 30

and thanks so much @leemah! as well, i will check out your way afterwards :)

Answer 31

You should have had

(21.3)/(75.3) = y/(360) @erin512

Answer 32

oh i forgot to isolate the denominator

Answer 33

No, you're confused @erin512, you isolate y

Answer 34

I don't know how you get this far without understanding proportions.

Answer 35

yes i mean i should have done 21.3/(2*pi*12)

Answer 36

but i did 21.3/2*pi*12 and didn't solve the 2*pi*12 part before i divided that by 21.3 do you know what i mean

Answer 37

@Leemah!, I focus on showing the relationship between sector, arc, and length of a circle with proportions.

Answer 38

@erin512, you need to learn how to do proportions first

Answer 39

yes

Answer 40

i know how to do them i just messed up here

Answer 41

but y=101.83 right?

Answer 42

http://www.wolframalpha.com/input/?i=solve%28%2821.3%29%2F%282*pi*12%29+%3D+y%2F360%2C+y%29

Answer 43

Close enough

Answer 44

i'll go over this again to make sure i understand it, thanks so much again

Answer 45

@Hero Won't you have to change to radian measure now?

The answer to your question is in degree format.

Answer 46

It is but, if she solves it the way I showed her originally, it would be in radian format

Answer 47

Ok, I guess I wasn't there the first time.

Answer 48

Yes, you were bro.

Answer 49

Remember, I solved a problem earlier describing how to get both the approximate and the exact answer