A survey team locates the ground position $T$ of a radio transmitter using two observation points $A$ and $B$ which lie on level horizontal ground. The distance $AB$ is $3.20\text{ km}$ The bearing of $B$ from $A$ is $090^\circ$ the bearing of $T$ from $A$ is $055^\circ$ and the bearing of $T$ from $B$ is $330^\circ$ Bearings are measured clockwise from north.

The antenna point $P$ is vertically above $T$ The angle of elevation of $P$ from $A$ is $4.0^\circ$