The four forces in the diagram are in equilibrium. Find the force F and cos θ.

To find the force $F$ and $\cos\theta$, we need to resolve all forces into their horizontal (x) and vertical (y) components. Since the system is in equilibrium, the sum of the x-components and the sum of the y-components must both be zero.

Let's define the angles with respect to the horizontal axis.

1. Force $F$: Acts in the second quadrant. The angle with the negative x-axis is $\theta$.

   • x-component: $-F \cos\theta$
   • y-component: $F \sin\theta$

2. Force $13 \text{ N}$: Acts in the first quadrant. The angle with the positive x-axis is $