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Conventional Polaroid time-of-flight (TOF) sonars provide object range measurements, but their wide beam widths limit the object bearing accuracy. We describe a first-order model that predicts the TOF readings from an object at a given range, bearing, and reflecting strength produced by the Polaroid 6500 series sonar ranging module connected to a 600 series electrostatic transducer. The model provides a simple method for solving the inverse problem of estimating these object parameters from conventional TOF data. Experimental results are given to demonstrate the model performance. Our model provides a reasonable fit for main-lobe data observed for objects with reflecting strengths that vary by 25 dB. An example of an inverse problem solution demonstrates the model can improve object range and bearing measurements, and can also estimate the object reflecting strength, a landmark feature useful for robot navigation tasks.