(i) Resolve forces horizontally and vertically:

Horizontal: \(7.5 \cos 60^\circ + 4.5 \cos 20^\circ = F \cos \theta\)

\(7.5 \sin 60^\circ - 4.5 \sin 20^\circ = F \sin \theta\)

Calculate: \(7.5 \cos 60^\circ + 4.5 \cos 20^\circ = 7.97861\)

\(7.5 \sin 60^\circ - 4.5 \sin 20^\circ = 4.95609\)

Use Pythagoras: \(F = \sqrt{7.98^2 + 4.96^2} = 9.39\) N

Use trigonometry: \(\theta = \arctan \left( \frac{4.96}{7.98} \right) = 31.8^\circ\)

(ii) Apply Newton's second law along AB:

\(9.5 \cos 30^\circ - 7.5 \cos 60^\circ - 4.5 \cos 20^\circ = m \times 1.5\)

Calculate: \(m = 0.166\) kg