To solve for \(F\) and \(\alpha\), we use the equilibrium condition, which states that the sum of the forces in any direction must be zero.

Resolve horizontally:

\(F \cos \alpha - 20 \cos 40 - 100 \sin 20 = 0\)

\(F \cos \alpha = 49.5229 \ldots\)

Resolve vertically:

\(F \sin \alpha + 20 \sin 40 - 100 \cos 20 = 0\)

\(F \sin \alpha = 81.1135 \ldots\)

Now, solve for \(F\):

\(F = \sqrt{(49.5229 \ldots)^2 + (81.1135 \ldots)^2}\)

\(F = 95.0\)

To find \(\alpha\):

\(\tan \alpha = \frac{81.1135 \ldots}{49.5229 \ldots}\)

\(\alpha = 58.6\)