1. ## finding theta

Can someone point out where I am going wrong in this problem?

Three forces are applied to an object, as indicated in the drawing. Force 1 has a magnitude of 33.0 newtons (33.0 N) and is directed 30.0° to the left of the +y axis. Force 2 has a magnitude of 16.0 N and points along the +x axis. What must be the magnitude and direction (specified by the angle θ in the drawing) of the third force 3 such that the vector sum of the three forces is 0 N? magnitude28.6 Nθ2°

The only thing I need to do is find theta. I thought it would work by doing tan^-1(28.6) but that gave me 88 degrees and it didn't work. Suggestions?

Thanks,
juventinoalex

2. the given sketch (for some reason, either an error or an intentional deception) is incorrectly depicted.

$\displaystyle F_2$ is a 16 N force in the positive x-direction.

$\displaystyle F_1$ has an x-component = 33cos(60) = 16.5 N in the negative x-direction.

for there to be equilibrium, F_3 should be in quad IV with an x-component to the right of 0.5 N.

if the problem is legit, then $\displaystyle \theta$ (as depicted) should be greater than 90 degrees.

3. To solve $\displaystyle \theta$, use the right angle tangent rule:

$\displaystyle tan(\theta) = \frac{opposite}{adjacent}$

As skeeter said, there must be a 0.5N force to the right and a 28.6N force downwards to balance everything out.

For me, I get $\displaystyle 88.998^{\circ}$ in quadrant IV, therefore:
$\displaystyle \theta = 91^{\circ}$