(i) To find the area of the shaded region BPDQ, we calculate the area of sector BPD and subtract the area of triangle BPD. The area of sector BPD is given by \(\frac{1}{2} \times 5^2 \times 1.2\). The area of triangle BPD is \(\frac{1}{2} \times 5^2 \times \sin 1.2\). Therefore, the area of the shaded region is:

\(2 \left[ \frac{1}{2} \times 5^2 \times 1.2 - \frac{1}{2} \times 5^2 \times \sin 1.2 \right] = 6.70\)

(ii) To find the length of PQ, we use the cosine rule in triangle APQ. The length of PQ is given by:

\(5 \cos 0.6\)

Then, subtract from 5:

\(5 - 5 \cos 0.6\)

Multiply by 2:

\(10(1 - \cos 0.6) = 1.75\)