Heights and Distances question bank (Maths)

The angle of elevation of the top $P$ of a vertical tower $PQ$ of height $10$ from a point $A$ on the horizontal ground is $45°$. Let $R$ be a point on $AQ$ and from a point $B$, vertically above $R$, the angle of elevation of $P$ is $60°$. If $\angle BAQ=30°,AB=d$ and the area of the trapezium $PQRB$ is $\alpha$, then the ordered pair $\left(d,\alpha \right)$ is

A spherical gas balloon of radius $16$ meter subtends an angle $60°$ at the eye of the observer $A$ while the angle of elevation of its center from the eye of $A$ is $75°$. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :