The angle of elevation of the top of a tower from a point $A$ due north of it is $\alpha$ and from a point $B$ at a distance of 9 units due west of $A$ is $\cos ^ { - 1 } \left( \frac { 3 } { \sqrt { 13 } } \right)$. If the distance of the point $B$ from the tower is 15 units, then $\cot \alpha$ is equal to\\
(1) $\frac { 6 } { 5 }$\\
(2) $\frac { 9 } { 5 }$\\
(3) $\frac { 4 } { 3 }$\\
(4) $\frac { 7 } { 3 }$