Isn't it just quicker to solve the above problems by finding the arc length first by Arc = radius x angle? Then subtract this amount from 2 Pi then multiply the result by the radius? Thanks Best regards

You cannot find the arc length of CD until you have established a measure for angle CPD or a combined measure of all other angles.

I wish there was a little screen we can use to do the work on the computer instead of wasting paper.

You can use the *Math Input Panel* app that is already installed on Windows, if your device is running a Windows OS (Vista/7/8/8.1/10). Hope this helps!

Is there are way to tell that CD (in question 3) was asking for DC in the clockwise direction, rather than CD in the anti-clockwise direction? I got my answer (correct) only by looking at the answers provided. Is there a convention that says, 'looking for angles is always clockwise'? Or did I miss something such as CD clockwise would be written as CAD,or CBAED, or something?

When we write an arc with only two letters it implies that it is a minor arc (under 180°) so in this case CD is the arc that goes anti-clockwise from C to D, in other words the small arc. And yes you are right about the clockwise notation : we typically use a third point to write major arcs (over 180°) in order to avoid any confusion, so CD clockwise could be CAD, CBE and so on.

So arc length (in radians) is just `length = angle*radius`?

That is correct! For example, the arc length of an angle of 2/5 radians in a circle with a radius of 5 units is 2 units.

why don't the options have 85/2 pi radians? is it a convention not to write radians or something?

radians is a measure of angles, so if you were measuring a length, you would not use radians, the answer would be in "units" not radians. When you divide the arc measure/radians in a circle, both units are radians, and they cancel, so when you multiply by the circumference in units, then the answer is in units.

The end part of changing 7pi/36 to 35pi/18, All i did was multiply 7pi/36 by 10, the radius, then simplify. Is this an incorrect form/doesn't work in every situation?

This is valid, the arc length will always be the subtended angle multiplied by the radius.

In problem 3, how does 7/36π ⋅ 20π/2π = 35/18π ? I don't know what process is used to get from before to after.

When you multiply the fractions, you get 7*20*pi/36*2*pi*pi or 140pi/72pi^2. Divide both sides by their greatest common factor, 4pi, and you get a simplified 35/18pi. If you need more help, you can watch one of KA's videos on multiplying and simplifying fractions. Keep exploring!

What happens if the central angle is in degrees and the radius is in feet? How do you solve it ?

It should not change anything, the examples use the generic term units, so if you said, for example, in the first problem 25 feet instead of 25 units, when you set up a proportion and solve, the answer would be in feet rather than units.

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Geometry (all content)

Course: Geometry (all content) > Unit 14

Lesson 5: Arc length (from radians)

Challenge problems: Arc length (radians) 1

Google Classroom

Solve three challenging problems that ask you to find arc length without directly giving you the arc measure.

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Robert Dunn
Posted 7 years ago. Direct link to Robert Dunn's post “Isn't it just quicker to ...”
Isn't it just quicker to solve the above problems by finding the arc length first by Arc = radius x angle?
Then subtract this amount from 2 Pi then multiply the result by the radius?

Thanks
Best regards
Button navigates to signup pageButton navigates to signup page
(33 votes)
Answer
- 108464
  Posted 7 years ago. Direct link to 108464's post “You cannot find the arc l...”
  You cannot find the arc length of CD until you have established a measure for angle CPD or a combined measure of all other angles.
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  (6 votes)
ryan garcia
Posted 7 years ago. Direct link to ryan garcia's post “I wish there was a little...”
I wish there was a little screen we can use to do the work on the computer instead of wasting paper.
Button navigates to signup pageComment on ryan garcia's post “I wish there was a little...”
(20 votes)
Answer
- Brody Stanley
  Posted 7 years ago. Direct link to Brody Stanley's post “You can use the *Math Inp...”
  You can use the Math Input Panel app that is already installed on Windows, if your device is running a Windows OS (Vista/7/8/8.1/10). Hope this helps!
  Button navigates to signup page
  (22 votes)
mathman
Posted 7 years ago. Direct link to mathman's post “Is there are way to tell ...”
Is there are way to tell that CD (in question 3) was asking for DC in the clockwise direction, rather than CD in the anti-clockwise direction? I got my answer (correct) only by looking at the answers provided. Is there a convention that says, 'looking for angles is always clockwise'? Or did I miss something such as CD clockwise would be written as CAD,or CBAED, or something?
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- Dan V
  Posted 7 years ago. Direct link to Dan V's post “When we write an arc with...”
  When we write an arc with only two letters it implies that it is a minor arc (under 180°) so in this case CD is the arc that goes anti-clockwise from C to D, in other words the small arc.
  And yes you are right about the clockwise notation : we typically use a third point to write major arcs (over 180°) in order to avoid any confusion, so CD clockwise could be CAD, CBE and so on.
  Button navigates to signup page
  (6 votes)
laddhanishtha
Posted 6 years ago. Direct link to laddhanishtha's post “why don't the options hav...”
why don't the options have 85/2 pi radians? is it a convention not to write radians or something?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “radians is a measure of a...”
  radians is a measure of angles, so if you were measuring a length, you would not use radians, the answer would be in "units" not radians. When you divide the arc measure/radians in a circle, both units are radians, and they cancel, so when you multiply by the circumference in units, then the answer is in units.
  Button navigates to signup page
  (5 votes)
MasonG
Posted 6 years ago. Direct link to MasonG's post “So arc length (in radians...”
So arc length (in radians) is just
length = angle*radius?
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(3 votes)
Answer
- Alexander Melby
  Posted 4 years ago. Direct link to Alexander Melby's post “That is correct! For exam...”
  That is correct! For example, the arc length of an angle of 2/5 radians in a circle with a radius of 5 units is 2 units.
  Button navigates to signup page
  (2 votes)
Nathan Yao
Posted 5 years ago. Direct link to Nathan Yao's post “Can somebody explain the ...”
Can somebody explain the logic behind the way of solving all of these questions, I feel like I am just memorizing some formulas , thank you!
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(3 votes)
Answer
- Shreyas
  Posted 4 years ago. Direct link to Shreyas's post “The logic behind behind f...”
  The logic behind behind finding arc lengths and arc measures is related to finding the measure of the central angle that intercepts the arc. As Khan Academy solves them using proportions, it is one way but if you're not finding yourself finding comfortable with proportions as in arc length/circumference = arc measure/360, you can use other ways too.
  Most questions ask you to find arc lengths and arc measures, which you can easily find by finding the measure of the central angle the arc subtends and use the 1 or 2 formulas to find arc length.
  Button navigates to signup page
  (1 vote)
Chris Morrissy
Posted 7 years ago. Direct link to Chris Morrissy's post “The end part of changing ...”
The end part of changing 7pi/36 to 35pi/18,
All i did was multiply 7pi/36 by 10, the radius, then simplify.
Is this an incorrect form/doesn't work in every situation?
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(1 vote)
Answer
- hergettj
  Posted 7 years ago. Direct link to hergettj's post “This is valid, the arc le...”
  This is valid, the arc length will always be the subtended angle multiplied by the radius.
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  (2 votes)
Journey
Posted 7 years ago. Direct link to Journey's post “um can someone explain ar...”
um can someone explain arc length
central angle
circumference
sorry but sal didnt really hit the subject like i thought
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(1 vote)
Answer
Ethan Brock
Posted 5 years ago. Direct link to Ethan Brock's post “In problem 3, how does 7...”
In problem 3, how does
7/36π ⋅ 20π/2π = 35/18π
?
I don't know what process is used to get from before to after.
Button navigates to signup pageComment on Ethan Brock's post “In problem 3, how does 7...”
(1 vote)
Answer
- Joanna G
  Posted 5 years ago. Direct link to Joanna G's post “When you multiply the fra...”
  When you multiply the fractions, you get 7*20*pi/36*2*pi*pi or 140pi/72pi^2. Divide both sides by their greatest common factor, 4pi, and you get a simplified 35/18pi. If you need more help, you can watch one of KA's videos on multiplying and simplifying fractions. Keep exploring!
  Button navigates to signup page
  (2 votes)
ratwoo3460
Posted 3 years ago. Direct link to ratwoo3460's post “What happens if the centr...”
What happens if the central angle is in degrees and the radius is in feet? How do you solve it ?
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(1 vote)
Answer
- David Severin
  Posted 3 years ago. Direct link to David Severin's post “It should not change anyt...”
  It should not change anything, the examples use the generic term units, so if you said, for example, in the first problem 25 feet instead of 25 units, when you set up a proportion and solve, the answer would be in feet rather than units.
  Button navigates to signup page
  (2 votes)

Geometry (all content)

Course: Geometry (all content) > Unit 14

Challenge problems: Arc length (radians) 1

Problem 1

Problem 2

Problem 3

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