Heights and Distances question bank (Quantitative Aptitude)

$A$ tower is $30 \ m$ high. An observer from the top of the tower makes an angle of depression of $60^{\circ}$ at the base of the building and an angle of depression of $45^{\circ}$ at the top of the building. What is the height of the building in metres?

Two towers of equal height stand on either side of a wide road which is $100 \, m$ wide. At a point on the road between the towers, the angles of elevation of the tops of the towers are $60^{\circ}$ and $30^{\circ}$. Find their heights in metres. (in $\sqrt{3}$)