We study the problem of placing bearing sensors so as to estimate the location of a target in a square environment. We consider sensors with unknown but bounded noise: the true location of the target is guaranteed to be in a 2α-wedge around the measurement, where α is the maximum noise. The quality of the placement is given by the area or diameter of the intersection of measurements from all sensors in the worst-case (i.e. regardless of the target's location). We study the bi-criteria optimization problem of placing a small number of sensors while guaranteeing a worst-case bound on the uncertainty. Our main result is a constant-factor approximation: We show that in general when α ≤ Π/4, at most 9n* sensors placed on a triangular grid has diameter and area uncertainty of at most 5.88U D* and 7.76UA* respectively, where n*,UD* and UA* are the number of sensors, diameter and area uncertainty of an optimal algorithm. In obtaining these results, we present some structural properties which may be of independent interest. We also show that in the triangular grid placement, only a constant number of sensors need to be activated to achieve the desired uncertainty, a property that can be used for designing energy/bandwidth efficient sensor selection schemes.