Question

Four ropes are tied to a stake, and each is pulled toward a compass direction, N, S, E, or W. A force of 13 N is applied to the rope pulled toward the east. Forces of 23, 25, and 38 N are applied toward the south, west, and north, respectively. What is the direction of the net force exerted on the stake by the ropes?

Answer 1

Fn = (13-25) + i(38-23),
Fn = -12 + i15,

tanAr = Y/X = 15/-12 = -1.25,
Ar = -51.34 deg.
A = 180 + (-51.34) = 128.7 deg.