(i) The work done by the pulling force is calculated using the formula:

\(\text{Work Done} = Fd \cos \beta\)

where \(F = 30 \text{ N}\), \(d = 20 \text{ m}\), and \(\beta = 10^{\circ}\).

\(\text{Work Done} = 30 \times 20 \times \cos 10^{\circ} = 591 \text{ J}\)

(ii) The gain in potential energy is given by:

\(\text{PE gain} = mgh\)

where \(m = 8 \text{ kg}\), \(g = 10 \text{ m/s}^2\), and \(h = d \sin \alpha\) with \(\alpha = 15^{\circ}\).

\(h = 20 \times \sin 15^{\circ}\)

\(\text{PE gain} = 8 \times 10 \times 20 \times \sin 15^{\circ} = 414 \text{ J}\)

(iii) The work done against the resistance to motion of the box is the difference between the work done by the pulling force and the gain in potential energy:

\(\text{Work done against resistance} = 591 \text{ J} - 414 \text{ J} = 177 \text{ J}\)