(i) To find the angle \(\angle POQ\) in radians, use the formula for arc length: \(s = r\theta\). Given \(s = 9\) cm and \(r = 5\) cm, we have:

\(9 = 5\theta\)

\(\theta = \frac{9}{5} = 1.8 \text{ rad}\)

(ii) To find the length of \(PT\), consider triangle \(POT\). The angle \(\angle POT\) is half of \(\angle POQ\), so \(\angle POT = \frac{1.8}{2} = 0.9 \text{ rad}\). Using the tangent function:

\(PT = 5 \tan(0.9) \approx 6.30 \text{ cm}\)

(iii) To find the area of the shaded region, first calculate the area of sector \(POQ\):

\(\text{Area of sector} = \frac{1}{2} \times 5^2 \times 1.8 = 22.5 \text{ cm}^2\)

Next, calculate the area of triangle \(POT\):

\(\text{Area of } POT = \frac{1}{2} \times 5 \times 6.30 = 15.75 \text{ cm}^2\)

The shaded area is twice the area of triangle \(POT\) minus the area of the sector:

\(\text{Shaded area} = 2 \times 15.75 - 22.5 = 9.00 \text{ cm}^2\)