The angle of elevation of the top of a vertical tower from a point $A,$ due east of it is $45^0$. The angle of elevation of the top of the same tower from a point $ B$, due south of $A$ is $30^0$. If the distance between $A$ and $B$ is $54 \sqrt 2$ m , then the height of the tower (in metres), is :

Question

$\begin{array}{1 1}(1)\; 36 \sqrt 3 \\ (2)\; 54 \\ (3)\; 54 \sqrt 3 \\ (4)\;108 \end{array} $