Physics
posted by Lexie on .
Five forces act on an object.
(1) 63 N at 90°
(2) 40 N at 0°
(3) 83 N at 270°
(4) 40 N at 180°
(5) 50 N at 60°
What are the magnitude and direction of a sixth force that would produce equilibrium?

find sum in x direction
63 cos 90 + 40 cos 0 + 83 cos 270 + 40 cos 180 + 50 cos 60
=50 cos 60 = 25 N at 0 deg
find sum in y direction
63 sin 90 + 40 sin 0 etc = 23.3
tan theta = 23.3/25 = .932
theta = 43
we want equal and opposite
so 43 + 180 = 223 degrees
magnitude = sqrt (625+543)
= 34.2 Newtons 
For others to be able to solve:
I'm using variables since I'm use to computer science
N = newtons // number after is force number, x is angle
T1 = N1 cos A, N2 cos A, N3 cos A, etc
T2 = N1 sin A, N2 sin A, N3 sin A, etc
D = TAN1(T1/T2) //use calculator
direction = D + 180
magnitude = sqrt(T1ˆ2 + T2ˆ2)
I liked your answer Damon.