Detect when a point belongs to a bounding box with distances I have a box with known bounding coordinates (latitudes and longitudes): latN, latS, lonW, lonE.
I have a mystery point P with unknown coordinates. The only data available is the distance from P to any point p. dist(p,P).`
I need a function that tells me whether this point is inside or outside the box.

The distance measurement from any point gives you a circle around that point as a locus of possible positions of $P$.
Make any such measurement from a point $A$.
If the question is not settled after this (i.e. if the circle crosses the boundary of the rectangle), make a measurement from any other point $B$. The two intersecting circles leave only two possibilities for the location of $P$.
If you are lucky, both options are inside or both outside the rectnagle and we are done.
Otherwise, a third measurement taken form any point $C$ not collinear with $A$ and $B$ will settle the question of exact position of $P$ (and after that we easily see if $P$ is inside or not.
One may wish to choose the first point $A$ in an "optimal" faschion such that the probability of a definite answer is maximized. 
While this requires knowledge about soem a prioi distribution where $P$ might be, the center of the rechtangle seems like a good idea. The result is nondecisive only if the measured distance is between half the smallest side of the rectangle and half the diagonal of the rectangle.
