Hello, I have been working diligently on the circle/arc module, and have gotten to the test area, where I am encountering a few problems--after revealing the solution, and plugging the values in sundry ways, still I am not getting this equation, please help - θ/360 = s / c θ/360 = 5/6π/20π θ = 15 ----------- the solution says this should be 15 degrees, and I keep getting 18, please can someone explain the steps exactly. thanx so much. j

θ/360=5/6pi/20pi So θ/360=5/120 θ=3*5=15

How did the 18 go from the top to the bottom

Dividing by 20𝜋 is the same as multiplying by 1∕(20𝜋). Also, we can write 𝜋 as 𝜋∕1 So, (221∕18)𝜋∕(20𝜋) = 221∕18⋅𝜋∕1⋅1∕(20𝜋) Now we have a product of fractions, which we know is the same as the product of the numerators divided by the product of the denominators. 221∕18⋅𝜋∕1⋅1∕(20𝜋) = (221⋅𝜋⋅1)∕(18⋅1⋅20𝜋)

what would be some examples of why we'd need to know this? Or what profession rather would someone use this sort of geometry? Please and thanks

a draftsman\designer would use degrees and the machinist would read the print in degrees to make the part. Any tradesman that fabricates things would use degrees. Radians are left to the sciences.

At 1:06 in the video Sal said " in terms of 2 pi radians around the circle," What are radians?

Radian is one of the unit to measure angles. 1 radian = 180/pi degrees 2pi radians= 360 degrees 1 degree = pi/180 radians To know more about it see the videos on following link : https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/introduction-to-radians

If two chords of a circle are equal , than their corresponding arcs are equal?

Yes, if the chords are the same length on the same size circle.

I was just wondering if theta was just another way of replacing an unknown value (variable).

Yes, Greek letters are commonly used for variables to represent an unknown/solvable angle.

why did he multiply both sides by 360 degrees?

He needed to get theta by itself, so he multiplied both sides by 360

Why did 18 become the denomonater of the final equation?

221pi/18/20pi is a fraction divided by another fraction, you can rewrite it as 221pi/18 divided by 20pi/1. (18 is in the denominator of the first fraction.) To divide a fraction by a fraction, we multiply by it's reciprocal, so 221pi/18 * 1/20pi. Which makes, 221ph/18*20ph. The videos in this playlist can it explain the concept better: https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/conceptual-understanding-of-dividing-fractions-by-fractions https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/another-dividing-fractions-example

one thing i find interesting is that he never shows how to find arc length.... can someone please explain?

You use the inner angle to find it. Someone with a better expertise can explain to you easier (I am looking at people who glance over these comments and could answer it).

Main content

High school geometry

Course: High school geometry > Unit 8

Lesson 3: Arc length (from degrees)

Subtended angle from arc length

Name: Subtended angle from arc length
Uploaded: 2013-08-14T20:58:27Z
Description: Watch Sal solve an example where he finds the central angle given arc length.

Google Classroom

Watch Sal solve an example where he finds the central angle given arc length. Created by Sal Khan.

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James Forest
Posted 10 years ago. Direct link to James Forest's post “Hello, I have been workin...”
Hello, I have been working diligently on the circle/arc module, and have gotten to the test area, where I am encountering a few problems--after revealing the solution, and plugging the values in sundry ways, still I am not getting this equation, please help -

θ/360 = s / c

θ/360 = 5/6π/20π

θ = 15

-----------
the solution says this should be 15 degrees, and I keep getting 18, please can someone explain the steps exactly. thanx so much.

j
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(12 votes)
Answer
- Jimmy
  Posted a year ago. Direct link to Jimmy's post “θ/360=5/6pi/20pi So θ/360...”
  θ/360=5/6pi/20pi
  So θ/360=5/120
  θ=3*5=15
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  (2 votes)
akiio25
Posted 2 years ago. Direct link to akiio25's post “How did the 18 go from th...”
How did the 18 go from the top to the bottom
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(11 votes)
Answer
- Jerry Nilsson
  Posted 2 years ago. Direct link to Jerry Nilsson's post “Dividing by 20𝜋 is the s...”
  Dividing by 20𝜋 is the same as multiplying by 1∕(20𝜋).
  Also, we can write 𝜋 as 𝜋∕1
  
  So, (221∕18)𝜋∕(20𝜋) = 221∕18⋅𝜋∕1⋅1∕(20𝜋)
  
  Now we have a product of fractions, which we know is the same as the product of the numerators divided by the product of the denominators.
  221∕18⋅𝜋∕1⋅1∕(20𝜋) = (221⋅𝜋⋅1)∕(18⋅1⋅20𝜋)
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  (7 votes)
Andrew Valdez
Posted 10 years ago. Direct link to Andrew Valdez 's post “what would be some exampl...”
what would be some examples of why we'd need to know this? Or what profession rather would someone use this sort of geometry? Please and thanks
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(8 votes)
Answer
- Art
  Posted 6 years ago. Direct link to Art's post “a draftsman\designer woul...”
  a draftsman\designer would use degrees and the machinist would read the print in degrees to make the part. Any tradesman that fabricates things would use degrees. Radians are left to the sciences.
  Button navigates to signup page
  (5 votes)
Ishan Khare
Posted 8 years ago. Direct link to Ishan Khare's post “At 1:06 in the video Sal ...”
At
1:06
in the video Sal said " in terms of 2 pi radians around the circle," What are radians?
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(5 votes)
Answer
- Kartik Nagpure
  Posted 8 years ago. Direct link to Kartik Nagpure's post “Radian is one of the unit...”
  Radian is one of the unit to measure angles.
  1 radian = 180/pi degrees
  2pi radians= 360 degrees
  1 degree = pi/180 radians
  To know more about it see the videos on following link :
  https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/introduction-to-radians
  Comment on Kartik Nagpure's post “Radian is one of the unit...”
  (10 votes)
blayseh
Posted 8 years ago. Direct link to blayseh's post “I don't quite understand ...”
I don't quite understand the process when you put everything over each other and solve. Is there a simpler way of thinking about it or solving it?
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(6 votes)
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surens68
Posted 10 years ago. Direct link to surens68's post “If two chords of a circle...”
If two chords of a circle are equal , than their corresponding arcs are equal?
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(4 votes)
Answer
- Sai M
  Posted 9 years ago. Direct link to Sai M's post “Yes, if the chords are th...”
  Yes, if the chords are the same length on the same size circle.
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  (2 votes)
Vishwas
Posted 6 years ago. Direct link to Vishwas's post “I was just wondering if t...”
I was just wondering if theta was just another way of replacing an unknown value (variable).
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(3 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “Yes, Greek letters are co...”
  Yes, Greek letters are commonly used for variables to represent an unknown/solvable angle.
  Comment on David Severin's post “Yes, Greek letters are co...”
  (3 votes)
walid islam
Posted 9 years ago. Direct link to walid islam's post “why did he multiply both ...”
why did he multiply both sides by 360 degrees?
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(2 votes)
Answer
- Silver Wolf
  Posted 9 years ago. Direct link to Silver Wolf's post “He needed to get theta by...”
  He needed to get theta by itself, so he multiplied both sides by 360
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  (4 votes)
Calum Spreiter Cook
Posted 9 years ago. Direct link to Calum Spreiter Cook's post “Why did 18 become the den...”
Why did 18 become the denomonater of the final equation?
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(2 votes)
Answer
- Gigi
  Posted 9 years ago. Direct link to Gigi's post “221pi/18/20pi is a fracti...”
  221pi/18/20pi is a fraction divided by another fraction, you can rewrite it as 221pi/18 divided by 20pi/1. (18 is in the denominator of the first fraction.) To divide a fraction by a fraction, we multiply by it's reciprocal, so 221pi/18 * 1/20pi. Which makes, 221ph/18*20ph.
  
  The videos in this playlist can it explain the concept better:
  https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/conceptual-understanding-of-dividing-fractions-by-fractions
  
  https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/another-dividing-fractions-example
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  (2 votes)
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Posted 8 years ago. Direct link to Troyal Diefenderfer|Firekit|BeamNG.Drive Mod tester|'s post “one thing i find interest...”
one thing i find interesting is that he never shows how to find arc length....

can someone please explain?
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- Kairi
  Posted 3 years ago. Direct link to Kairi's post “You use the inner angle t...”
  You use the inner angle to find it. Someone with a better expertise can explain to you easier (I am looking at people who glance over these comments and could answer it).
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  (2 votes)

Video transcript

A circle has a circumference of 20 pi. It has an arc length of 221/18 pi. What is the central angle of the arc in degrees? So they're asking for this one. So this is the arc that they're talking about, that's 221/18 pi long. And they want to know this angle that it subtends, this central angle right over here. So we just have to remind ourselves that the ratio of this arc length to the entire circumference-- let me write that down-- the ratio of this arc length, which is 221/18 pi, to the entire circumference, which is 20 pi, is going to be equal to the ratio of this central angle, which we can call theta, the ratio of theta to 360 degrees if we were to go all the way around the circle. This will give us our theta in degrees. If we wanted it in radians, we would think of it in terms of 2 pi radians around the circle, but it was 360 degrees since we're in degrees. Now we just have to simplify. Now the easiest thing is just to multiply both sides times 360 degrees. So let's do that. So if we multiply the left-hand side by 360 degrees, we get 360 times 221 times pi over-- let's see, we have 18 times 20 times pi. And on the right-hand side, if we multiply it by 360, we are just left with theta. So we really just have to simplify this now. Pi divided by pi is going to be 1. 360 divided by 20, well, it's going to be the same thing as 36/2, which is the same thing as 18. And 18 divided by 18 is 1. So this all simplified to 221 degrees. Theta is 221 degrees.