This paper illustrates a new mechanism to determine the coordinates of the sensors using a beacon node and determines the definitive error associated with it. In UWSNs (underwater wireless sensor networks), actual and precise location of the deployed sensors which accumulate data is vital, because the accumulated data without the location information has less significance. Moreover it has limited value in the domain of location based services. In UWSN, trilateration or multilateration is exploited to assess the location of the deployed hosts; having three or more reference nodes to localize a deployed sensor is not pragmatic at all. On the other hand, non-linear equations are usually solved in conventional method where degree-of-freedom is uncertain to lead to an exclusive solution. In this paper, associated localization inaccuracies has been shown for a unique configuration where a single beacon is used to determine the coordinates of three deployed sensors simultaneously. Cayley-Menger determinant is used for the configuration and system of nonlinear distance equations have been linearized for better accuracy and convergence. Simulations with Euclidean distances validate the propounded model and reflect the acquired accuracies in sensors’ coordinates and bearings. Moreover, an experiment has been conducted with ultrasonic sensors in terrestrial environments to validate the proposed model; the associated inaccuracies were found to be generated from the distance measurement errors; on the other hand, considering Euclidean distances proves the model to be precise and accurate.