add the vectors (assuming N, S, E, W vectors), and the angles are measured clockwise from N 000 .
A=145 (cos190 N + sin 190 E)
B=75 (cos288 N + sin 288 E)
and so on. Then add all the N components, and all the E components.
R=M @ angle
where M= sqrt (sum N components ^2 + sum E components^2)
and angle= arc tan Ecomponents/Ncomponents
How do you do this?
A = 145 units @ 190o
B = 75 units @ 288o
C = 210 units @ 85o
D = 105 units @ 355o
Find the resultant vector:
R = A + B + C + D
3 answers
Vector = magnitude (cos T i + sin T j )
i is x direction
j is y direction
Thus
R x component =
145 cos 190 + 75 cos 288 + 210 cos 85 + 105 cos 355
R y component = 145 sin 190 + 75 sin 288 etc
in the end
|R| = sqrt (Rx^2 + Ry^2)
angle = tan^-1 (Ry/Rx)
i is x direction
j is y direction
Thus
R x component =
145 cos 190 + 75 cos 288 + 210 cos 85 + 105 cos 355
R y component = 145 sin 190 + 75 sin 288 etc
in the end
|R| = sqrt (Rx^2 + Ry^2)
angle = tan^-1 (Ry/Rx)
Note I assume x axis at 0
Bob used compass from N
Bob used compass from N