In the given figure, AT is a tangent to the circle with centre 'O' such that OT=4 cm and $\angle \mathrm{OTA}=30°$. Then AT is equal to:

It is given that AT is a tangent to the circle with centre 'O' such that OT=4 cm and $\angle \mathrm{OTA}=30°$ and we need to find the length of AT. 

On joining OA, it can be observed that $△\mathrm{OTA}$ is formed. Now, from $△\mathrm{OTA}$,

cos 30°=$\frac{\mathrm{AT}}{\mathrm{OT}}$

On substituting the given values, we get the length of AT as

$\Rightarrow \frac{\sqrt{3}}{2}=\frac{\mathrm{AT}}{4}$

$\Rightarrow \mathrm{AT}=2\sqrt{3}\mathrm{cm}$

Hence, the length of AT is $2\sqrt{3}$ cm.