1.81: Sector geometry and area

Figure 1 shows the sector $AOB$ of a circle with centre $O$ and radius 12 cm. The angle $AOB$ is $\theta$ radians and the area of the sector is $192\text{ cm}^2$.

Calculate

(a) the value of $\theta$, (2)

(b) the length, in cm, of the arc $AB$. (2)