Heights and Distances question bank (Maths)

From the top $A$ of a vertical wall $AB$ of height $30 \mathrm{m},$ the angles of depression of the top $P$ and bottom $Q$ of a vertical tower $PQ$ are ${15}^{\circ }$ and ${60}^{\circ }$ respectively, $B$ and $Q$ are on the same horizontal level. If $C$ is a point on $AB$ such that $CB\mathit{=}PQ\mathit{,}$ then the area (in ${\mathrm{m}}^2$) of the quadrilateral $BCPQ$ is equal to

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