Question

$PQ$ is a tower standing on a horizontal plane, $Q$ being its foot. Two points $A$ and $B$ are taken on the plane such that $AB=32$ and $\angle QAB$ is a right angle. It is found that $\cot PAQ=2/5$ and $\cot PBQ=3/5$, the height of the tower is

Answer 1

$h=\frac{AB}{\sqrt{(}{\cot }^2\beta -{\cot }^2\alpha )}=\frac{32}{\sqrt{(\frac{9}{25}-\frac{4}{25})}}=32\sqrt{5}$