Results 1 to 5 of 5

Math Help - Triangulation - Insufficient information?

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    2

    Triangulation - Insufficient information?

    Is there enough information to answer the following question:

    Two hikers are in the field out of each other's sight. They each have a cell phone and a compass. They want to meet together someplace along the straight line that connects their current positions. They call each other and agree on a distant landmark visible to each. They report to each other their bearing (Degrees from North) to the landmark. Can they now decide the proper bearing to walk to meetup in the shortest distance?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    1) Draw a distant landmark.
    2) Draw two rays emanating from the landmark. Make both rays in relatively the same direction, but leave some convenient small angle between them. Extend the rays as far as you dare. I recommend the edge of your drawing surface.
    3) Put a hiker on each ray.
    4) Grab one hiker and move it almost up to the landmark.
    5) Think about the path they would have to walk to meet up. You may wish to sketch this path lightly.
    6) Grab that same hiker and drag it back to the edge of your drawing surface.
    7) Think about the path they would have to walk to meet up. You may wish to sketch this path lightly.
    8) Now what?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,689
    Thanks
    617
    Hello, VictorL!

    Is there enough information to answer the following question?

    Two hikers are in the field out of each other's sight.
    They each have a cell phone and a compass.
    They want to meet together someplace along the straight line that connects their current positions.
    They call each other and agree on a distant landmark visible to each.
    They report to each other their bearing (degrees from North) to the landmark.
    Can they now decide the proper bearing to walk to meet up in the shortest distance?

    I say "No" . . . There is insufficient information.


    Suppose the landmark is "between" the two hikers, A and B.
    A diagram might look like this:


    Code:
                  L
                  o
                 *  *         :
                *     *       :
          :    *        *     :
          :   *           * β :
          :α *              * :
          : *                 o B
          :*                    *
        A o                       *
         *                          *
        *                             *
       *                                *
      * K                               M *

    The landmark is at L.
    The hikers are at A and B.

    A's heading to the landmark is N \alpha^oE
    B's heading to the landmark is N \beta^o W


    But A can be anywhere on the line LK.
    And B can be anywhere on the line LM.

    There is not enough information for their meeting.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2010
    Posts
    2
    Thanks.
    I can calculate the angle ALB (= \alpha + \beta), so I thought maybe I missed something.

    If I knew the distance between A and B? I think that should do it.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    No good. Still not unique.

    I would suggest having them walk for five minutes, track the distance travelled, and report the angles again.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 11th 2011, 02:32 AM
  2. triangulation
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: December 12th 2009, 07:00 PM
  3. Triangulation
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: December 11th 2009, 09:37 PM
  4. Triangulation of a Torus
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 25th 2009, 05:35 AM
  5. Insufficient information?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 5th 2009, 01:28 AM

Search Tags


/mathhelpforum @mathhelpforum