E4004 Surveying Computations A Two Missing Bearings

Derivation of Formula Consider line RS R S P If distances RP and PS are known the position of P is also known The intersection of two distances

Derivation of Formula But P could also lie on the other side of RS R S P P’ There are always two solutions in a two missing bearing problem

Derivation of Formula In the triangle RSP the bearing and distance RS will be known and the distances SP and PR will be provided R S P The direction of the bearings are important D2 MB MD D1 From a surveying viewpoint

Derivation of Formula Each angle can be solved with the cosine rule R S P D2 MB MD D1 We have a triangle with three known sides

Derivation of Formula R S P D2 MB MD D1 A B C a b c

Derivation of Formula R S P D2 MB MD D1 A B C a b c B C A c a b

Derivation of Formula The same formula apply for the second triangle R S P P’ MB MD D1 D2 Again the bearing directions are important

Derivation of Formula Angles R & S have been calculated R S P P’ MB MD R R S S B1 B2 B1’ B2’ LEFT of line RS RIGHT of line RS

Summary of Formula R S P P’ MB MD R R S S B1 B2 B1’ B2’ LEFT of line RSRIGHT of line RS