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Math Help - Determine distance between beacons

  1. #1
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    Determine distance between beacons

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    Last edited by jfontein; August 24th 2009 at 03:44 PM.
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  2. #2
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    Quote Originally Posted by jfontein View Post
    Hello,

    I have a practical problem which I can't solve (anymore). High-school and university (where I had some advanced math) is too long ago and I haven't kept up since...


    • There are 2 beacons (1) and (2).
    • The distance between (1) and (2) is known.
    • These 2 beacons 'create' 2 'virtual' beacons (A) and (B), each at the intersections at distance x from both beacon (1) and (2).
    • There are several candidates to become beacon number (3).
    • For each of these candidates the distance to the existing beacon (1) and (2) is known.
    • The ‘system’ doesn’t know coordinates.
    • To determine which candidate gets priority, there are some rules related to the distance between the candidate and beacon (A) and (B).


    • HOW can the distance to beacon (A) and (B) be calculated (easily) or HOW can this be (easily) approximated?
      • The calculation should be simple/easy as the calculation should be performed realtime/online: at the moment a candidate shows up, it should get feed back about its priority ranking within a few seconds.

    If I interpret your drawing correctly the beacons 1 and 2 are the midpoints of the white circles. If so you are dealing with 2 equilateral triangles with the side length r = distance between the two beacans.

    The distance AB is twice the height of a triangle:
    (Use Pythagorean theorem)

    h = \frac12 \cdot r \cdot \sqrt{3}

    Therefore

    |\overline{AB}|=2 \cdot \frac12 \cdot r \cdot \sqrt{3} =  r \cdot \sqrt{3}

    Tot ziens!
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  3. #3
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    Sorry, maybe my question wasn't clear enough. I am looking for the distance from a [random] candidate (3), with known distance to (1) and (2), to the beacons (A) and (B).

    [ I was still able to calculate the distance AB myself ;-) ]

    By the way, the triangle is not equilateral (or only by coincidence). The distance between the beacons (1) and (2) can vary.
    (I'll update the picture to give a clearer view on the situation).
    Last edited by mr fantastic; April 20th 2009 at 02:44 AM. Reason: Merged posts
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