If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## High school geometry

### Course: High school geometry>Unit 8

Lesson 3: Arc length (from degrees)

# Subtended angle from arc length

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

## Want to join the conversation?

• 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
• 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.
• 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)
• At in the video Sal said " in terms of 2 pi radians around the circle," What are radians?
• 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?
• 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