get the resultant of the following displacements 6 ft.southwest; 10 ft. northwest; 4 ft. southeast; 12 ft. northwest; and 3 ft. southwest. what is the direction of the resultant displacement?

Answer 1

All angles are measured CCW from +x-axis.
Fr = 6ft[225o] + 10[135] + 4[315] + 3[225].
Fr = (-4.24-4.24i)+(-7.07+7.07i)+(2.83-2.83i)+(-2.12-2.12i),
Add all hor. components. Then add all Ver. components:
Fr = -10.6 - 2.12i = 10.8ft[11.31o} S. of W. = 10.8ft[191.31o].