1.9: Right-angled triangle with an inscribed arc

The diagram shows the right-angled triangle $OAB$. The point $C$ lies on the line $OB$. Angle $OAB = \tfrac{\pi}{2}$ radians and angle $AOB = \theta$ radians. $AC$ is an arc of the circle, centre $O$, radius $12\text{ cm}$ and $AC$ has length $9.6\text{ cm}$.