They call it Height and Distance problem?

$P$ is top and $Q$ is the foot of a tower standing on a horizontal plane. $A$ is the foot a building standing beside the tower on the same horizontal plane, $B$ is another point on the building such that $AB$ is $32 \text{ m}$ . It is found that,

$\begin{cases} \cot(\angle PAQ)=\dfrac{2}{5} \\ \cot(\angle PBQ)=\dfrac{3}{5}\end{cases}$

If the height of tower (in meters) is in the form $a\sqrt{b}-c$ where $a,b,c \in \mathbb{N}$ and $b$ is square-free, then find $a+b+c$ .