Results 1 to 9 of 9

Math Help - Arc length and chord length

  1. #1
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1

    Arc length and chord length

    Does anyone know how to find the length of a chord knowing the radius of the circle and the arc length? Without using trigonometry.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    Do you have a specific problem?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    All right, why don't I just give you the whole thing.

    30 knights sit at King Arthur's round table. The table has a radius of 12 ft. Each knight has a lance that is 10 ft long. As King Arthur walks by each knight raises his lance and taps the lance of those it can reach. How many neighboring lances can one knight touch?

    The student that asked this problem (elsewhere) is in 9th grade doing Geometry, and thus cannot use Trigonometry. I'm stumped!

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Dec 2007
    From
    Melbourne
    Posts
    428
    I suspect this might be considered cheating, but drawing a reasonably accurate scale diagram and using a piece of string to measure the arc length could work.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member JaneBennet's Avatar
    Joined
    Dec 2007
    Posts
    293
    I think the only way to solve the problem without using trigonometry is to draw a diagram. What you do is draw a circle of radius 12, mark 30 equally spaced points on the circumference, then draw a circle of radius 20 with any one of these points as centre. (Each knight can touch the lance of another knight up to 20 ft away if both knights use their lances.) Then you just count how many points are contained in the second circle. (I think the answer is 18.)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    It seems to me that in order to be able to find the length that number (the length) needs to be a constructible number if you are only using geometry without triginometry. But that would mean some are impossible to construct for not all real numbers are constructible (for instance all real algebraic numbers of degree 3 over Q are not constructible). I am really not sure about this but the reasoning seems to work.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    Quote Originally Posted by JaneBennet View Post
    [FONT=Times New Roman]What you do is draw a circle of radius 12, mark 30 equally spaced points on the circumference, then draw a circle of radius 20 with any one of these points as centre. (Each knight can touch the lance of another knight up to 20 ft away if both knights use their lances.)
    Here is a graph.
    Attached Thumbnails Attached Thumbnails Arc length and chord length-knights.gif  
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    I don't see any Teaching going on here . . .
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    Quote Originally Posted by Soroban View Post
    I don't see any Teaching going on here . . .
    Why does that surprise me? Oh yes, I got it: none of us gave a complete, worked out, ready to hand in solution. Teaching is measured by learning. If the student has nothing to do, no learning can possibly take place. Learning is active not passive. Learning mathematics is not a specter activity; the learner must be evolved in the activity. Why donít you review this entire thread? I think you would be surprised how much learning did go on. I, for one, learned a great deal about graphing the problem using a minimal edition of MathCad. Any student who uses such a CAS, would learn a great deal of mathematics in the simple act of modeling this problem as JaneBennet smartly suggested.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Arc Length and Chord Length
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 22nd 2010, 02:24 AM
  2. Replies: 1
    Last Post: September 15th 2010, 03:04 PM
  3. Chord length of a circle inscribed in a rectangle
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 23rd 2010, 03:56 AM
  4. how calculate chord length of ellipse.
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 2nd 2010, 03:54 AM
  5. Need help with chord length.
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 5th 2009, 11:44 AM

Search Tags


/mathhelpforum @mathhelpforum