Concise Proof of Tienstra’s Formula

Abstract

The resection problem consists in finding the location of an observer by measuring the angles subtended by lines of sight from this observer to three known stations. Many researchers and practitioners recognize that Tienstra’s formula provides the most compact and elegant solution to this problem. Unfortunately, all available proofs for this remarkable formula are intricate. This paper shows how, by using barycentric coordinates for the observer in terms of the locations of the stations, a neat and short proof is straightforwardly derived.