We consider the class of ad hoc networks, where a small percentage of the nodes are assumed to know their locations a priori and are denoted as reference nodes. Starting from the reference nodes, location information of other nodes are estimated in a hop by hop fashion. Beacon nodes are defined to be nodes that already have a location information (including the reference nodes). Using a two-dimensional cartesian coordinate system, we show that given a maximum of \pm \in error in the location of each of the beacon nodes and a maximum error of \pm \delta in each of the measured ranges along either axes, the location of a node can be computed within an error bound of \pm [3\in(1+\sqrt 2) + 2\delta] to \pm(3\in + 2\delta) along one axis and within \pm[2\delta(1+\sqrt 2) + 3\in] to \pm(3\in + 2\delta) along its orthogonal axis, by using the beacon selection algorithm proposed in this paper.