Villages ABCD are such that B is 4km due east of A C is 3km due to South of B and D is 4km S50W from C calculate the distance and bearing of A from aD

Question

Villages ABCD are such that B  is 4km due east of A C is 3km due to South of B and D is 4km S50W from C calculate the distance and bearing of A from aD

oobleck · Answer

Draw the diagram and add up the vectors.
If A is at (0,0) then
AD = AB+BC+CD = <4,0> + <0,-3> + <-4cos40°,-4sin40°> = <0.9358,-5.571>

and the bearing of A from D is SθE such that
tanθ = -5.571/0.9358