Where Am I ?

[Shawn Gibson]

[attachment=3635][attachment=3635]Here is an interesting problem. It may be fairly simple to solve but I am not having any luck with it so far. I am thinking of building a watering robot for my backyard garden. I want the robot to know where it is, so that it can avoid objects and add water to the right locations. I could use GPS but the resolution is just not good enough. I am thinking that if I were to place 3 beacons around the edge of the yard, the robot could be made to scan 360° and measure the angles between the beacons. Angles e,f and g.
By knowing the locations of the beacons (A,B and C), the robot should be able to calculate it's X and Y location from the Origin. The scanner will be able to differentiate between beacon A, B, and C by PWM frequency or Color.

I am sure this is not the only application where you would want to find a location by sighting 3 landmarks with know locations. Perhaps the surveyors do this all the time?

Special bonus brownie points, a hearty handshake, a pat on the back and the warm glow of victory if you can come up with a program to solve it. Say for the WP34S!

Any thoughts?
I welcome your comments.
I did include a diagram that should make the problem clearer.
Shawn