| Aspect | Platoon | Battalion |
|---|---|---|
| Size | 30-50 soldiers | 300-1000 soldiers |
| Command | Commanded by a Lieutenant | Commanded by a Lieutenant Colonel |
Platoon:
Battalion:
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD. 
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$. 