Help with Geocaching Triangulation problem - what is the best calc for this?

[Mark Gessner]

A Geocaching triangulation problem: Given three pairs of lat/lon coordinates, and a distance from each, find a third pair of unknown lat/lon coordinates.

Figured out how to do this by construction using a map and some dividers, but it seems that there must be a better way to do it by HP calculator. Which calculator would be ideal for this?

My wife grabbed her TI-83 and said it was best, but I maintain that one of my old HPs must be better. Problem is, I have so many of the damned things I can't choose which is best to solve the problem. See what you think:

http://www.geocaching.com/seek/cache_details.aspx?ID=20947&log=y&decrypt=y

-mark.

[Vieira, Luiz C. (Brazil)]

Hi;

I once dealt with a subject closer to this: given (M-1) coordinates and the expected area that define a M-coordinates polygon (a surface area), find the M_th coordinate (the "unknown" side could shift or rotate). I have the basic knowledge for surveying (I was a regular student at the surveying classes when I was at the university) so it was not too difficult to achieve a procedure.

My solution used a 2-unknown system and the matrices resources available with the calculator. Unfortunately, the final program does not belong to me and I will not disclose the listing. Anyway, the method I used to compute the unknown coordinate was developed by myself.

I used an HP48G at the time, but depending on how deep you want to go to solve the problem, any of these calculators can be used:

HP15C
HP28S
HP42S
HP48S/SX/G+/GX
HP49G

I do not know the HP39G and the HP40G, but I believe they can also be used. Even other calculators that do not have "resident" resources may be programmed to do so; the ones mentioned above may directly deal with matrices and complex numbers, if needed, without the needing of specific programs.

If you need more details and specific support, e-mail me.

Best regards.