How do you do this?

Question

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

Answer 1

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

Answer 2

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)

Answer 3

Note I assume x axis at 0
Bob used compass from N