Two forces are exerted on an object. A 33 N force acts at 215° and a 45 N force acts at 315°. What are the magnitude and direction of the equilibrant?

Answer 1

F1 + F2 + F3 = 0
33N[215o] + 45N[315] + F3 = 0
33*cos215+i33*sin215+45*cos315+i45*sin315+F3 = 0
23.33 - i18.93 + 31.82 - i31.82 + F3=0
55.15 - i50.75 + F3 = 0
F3=-55.15 + i50.75=sqr(-55.15^2+50.75^2)= 74.95 N. = The equilibrant.

Tan Ar = Y/X = 50.75/-55.15=-0.92022
Ar = -42.62o = Reference angle.
A = -42.62 + 180 = 137.4o = Direction.