To solve for \(F\) and \(\alpha\), we resolve the forces horizontally and vertically, using the fact that the forces are in equilibrium.

First, resolve horizontally:

\(2F + F \cos 60^\circ = 15 \cos \alpha\)

Next, resolve vertically:

\(F \sin 60^\circ = 15 \sin \alpha\)

Using these two equations, we can solve for \(F\) and \(\alpha\). From the mark scheme, we have:

\(F = 5.67\) and \(\alpha = 19.1\)

Alternatively, \(F = \frac{15 \sqrt{7}}{7}\).