From Wikipedia, the free encyclopedia
Trilateration is a method of determining the relative positions of objects using the geometry of triangles in a similar fashion as triangulation. Unlike triangulation, which uses angle measurements (together with at least one known distance) to calculate the subject's location, trilateration uses the known locations of two or more reference points, and the measured distance between the subject and each reference point. To accurately and uniquely determine the relative location of a point on a 2D plane using trilateration alone, generally at least 3 reference points are needed.
A mathematical derivation for the solution of a three-dimensional trilateration problem can be found by taking the formulae for three spheres and setting them equal to each other. To do this, we must apply three constraints to the centers of these spheres; all three must be on the z=0 plane, one must be on the origin, and one other must be on the x-axis. It is, however, possible to translate any set of three points to comply with these constraints, find the solution point, and then reverse the translation to find the solution point in the original coordinate system. |
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Below are four geocaches,chosen somewhat at random, based on their general area. I've listed their coordinates, and their distance from this cache(in nautical miles). Using this information you should be able to calculate the coordinates of this cache to within a few feet.
| GC1169: |
N47° 23.514' W121° 27.305', |
162.21064 nautical miles |
| GCH1M8: |
N49° 44.599' W117° 10.128', |
124.28627 nautical miles |
| GCGW5N: |
N46° 52.061' W113° 59.008', |
150.20682 nautical miles |
| GCYHXW: |
N46° 03.786' W118° 16.050', |
102.43015 nautical miles |
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The overall difficulty rating of this cache is based on the difficulty of the puzzle, if you calculate the correct coordinates the cache would be about a 2 or 2.5 difficulty. The terrain rating is based on "worst case", if you carefully select your route it would be about a 2.5.
If your calculated coordinates are within 50' of the cache location, they should verify correctly using the link below.
This cache is located on the ground, covered by pine needles and a single rock. It's not very winter friendly and would be a difficult find if there's snow on the ground.
