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.

I'm so confused about how to find the lengths and the videos just aren't helping me.

To find the length of an arc, you can apply the formula 2πr * θ / (2π) -> r * θ. 2πr is the circle circumference. θ / (2π) is the ratio of the angle of the arc to the whole circle (360 degree = 2π radian)

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.

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.

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!

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.

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.

How can an angle be measured in radians?

Radians are just a different way of measuring angles. The definition of what makes a radian a radian is complicated (sal explains why a radian is a radian in the previous lesson), but all you really need to know is that there are 2pi radians in 360 degrees. Using this, you can convert any angle measured in degrees into radians.

Main content

Course: High school geometry > Unit 8

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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ryan garcia
Posted 8 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...”
(27 votes)
Answer
- Brody Stanley
  Posted 8 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!
  Comment on Brody Stanley's post “You can use the *Math Inp...”
  (33 votes)
Robert Dunn
Posted 8 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
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(37 votes)
Answer
- 108464
  Posted 8 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.
  Button navigates to signup page
  (5 votes)
mathman
Posted 8 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 8 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
  (7 votes)
Maggie Fonseca
Posted 10 months ago. Direct link to Maggie Fonseca's post “I'm so confused about how...”
I'm so confused about how to find the lengths and the videos just aren't helping me.
Button navigates to signup pageComment on Maggie Fonseca's post “I'm so confused about how...”
(6 votes)
Answer
- joshua
  Posted 9 months ago. Direct link to joshua's post “To find the length of an ...”
  To find the length of an arc, you can apply the formula 2πr * θ / (2π)
  -> r * θ.
  2πr is the circle circumference.
  θ / (2π) is the ratio of the angle of the arc to the whole circle (360 degree = 2π radian)
  Button navigates to signup page
  (3 votes)
laddhanishtha
Posted 7 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?
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(4 votes)
Answer
- David Severin
  Posted 7 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
  (6 votes)
MasonG
Posted 7 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 5 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)
Chris Morrissy
Posted 8 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?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- hergettj
  Posted 8 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.
  Button navigates to signup page
  (4 votes)
Nathan Yao
Posted 6 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 5 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
  (2 votes)
205744
Posted a year ago. Direct link to 205744's post “How can an angle be measu...”
How can an angle be measured in radians?
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(2 votes)
Answer
- (YC) DoD
  Posted 10 months ago. Direct link to (YC) DoD's post “Radians are just a differ...”
  Radians are just a different way of measuring angles. The definition of what makes a radian a radian is complicated (sal explains why a radian is a radian in the previous lesson), but all you really need to know is that there are 2pi radians in 360 degrees. Using this, you can convert any angle measured in degrees into radians.
  Button navigates to signup page
  (3 votes)
Journey
Posted 8 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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(2 votes)
Answer

Course: High school geometry > Unit 8

Challenge problems: Arc length (radians) 1

Problem 1

Problem 2

Problem 3

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