Since the forces are in equilibrium, the sum of the forces in both the horizontal and vertical directions must be zero.

Resolving horizontally:

\(F \cos \alpha = 40 \sin 30^\circ + 20 \sin 60^\circ - 50 \sin 45^\circ\)

\(F \cos \alpha = 1.965 \ldots\)

Resolving vertically:

\(F \sin \alpha = 50 \cos 45^\circ + 20 \cos 60^\circ - 40 \cos 30^\circ\)

\(F \sin \alpha = 10.714 \ldots\)

Using Pythagoras' theorem to find \(F\):

\(F = \sqrt{(1.965 \ldots)^2 + (10.714 \ldots)^2} = 10.9 \text{ N}\)

To find \(\alpha\):

\(\alpha = \arctan\left(\frac{10.714 \ldots}{1.965 \ldots}\right) = 79.6^\circ\)