(a) To find the values of \(F\) and \(G\) when the forces are in equilibrium, resolve the forces vertically and horizontally.

Vertically: \(G \sin 60^\circ + 2F \sin 40^\circ - 10 = 0\)

Horizontally: \(F + G \cos 60^\circ - 2F \cos 40^\circ = 0\)

Solving these equations simultaneously gives \(F = 4.53\) and \(G = 4.82\).

(b) Given \(F = 3\), resolve the forces parallel to the 10N force and equate this expression to zero:

\(G \sin 60^\circ + 2 \times 3 \sin 40^\circ - 10 = 0\)

Solving for \(G\) gives \(G = 7.09\) to 3 significant figures.