(i) To find the value of C, we use the triangle of forces. The horizontal component of the applied force is given by:

\(F = 4 \cos 30^{\circ}\)

The vertical component of the applied force is:

\(R = 10 - 4 \sin 30^{\circ}\)

Using the cosine rule for the triangle of forces:

\(C^2 = (4 \cos 30^{\circ})^2 + (10 - 4 \sin 30^{\circ})^2\)

Calculating gives:

\(C = 8.72\)

(ii) The coefficient of friction \(\mu\) is given by:

\(\mu = \frac{4 \cos 30^{\circ}}{10 - 4 \sin 30^{\circ}}\)

Calculating gives:

Coefficient is 0.433 (accept 0.43)