Heights and Distances question bank (Maths)

The angle of elevation of the top $P$ of a tower from the feet of one person standing due south of the tower is ${45}^{°}$ and from the feet of another person standing due west of the tower is ${30}^{°}$. If the height of the tower is $5$ meters, then the distance (in meters) between the two persons is equal to

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