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

A horizontal park is in the shape of a triangle $OAB$ with $AB=16$. A vertical lamp post $OP$ is erected at the point $O$ such that $\angle PAO=\angle PBO=15°$ and $\angle PCO=45°$, where $C$ is the midpoint of $AB$. Then ${\left(OP\right)}^2$ is equal to