Resolve horizontally and vertically, using equilibrium:

\[20\cos\theta=2F\cos30^\circ=\sqrt3F,\qquad20\sin\theta=F+2F\sin30^\circ=2F.\]

Divide the second equation by the first: \[\tan\theta=\frac2{\sqrt3}\quad\Longrightarrow\quad\boxed{\theta=49.1^\circ}\quad\text{(3 s.f.)}.\]

Square and add the resolved equations: \[400=3F^2+4F^2=7F^2\quad\Longrightarrow\quad F=\frac{20}{\sqrt7}=\boxed{7.56}\quad\text{(3 s.f.)}.\]