Question

A box is pulled in three directions but remains stationary. One rope pulls South with a force of 210 N. Another rope pulls Northwest and the third rope pulls East. What is the magnitude of the force from the third rope that pulls East?

Answer 1

$$\bold{F=F_1+F_2+F_3=0}\\ 0=(0,-210)+F_2(-\cos{45},\sin{45})+(F_3,0)\\ F_3=\frac{\sqrt{2}}{2}F_2=210\ N$$