There is a flag-post on the top of a $10 \, m$ high tower. From a point on the ground,the angle of elevation of the top of the tower is $45^{\circ}$ and that of the top of the flag-post is $60^{\circ}$. Find the height of the flag-post. (in $, m$)

An erect tree is $300\, m$ away from a hill. If the height of the hill is $300\, m$,find the angle of depression of the base of the tree from the top of the hill. (in $^{\circ}$)

From a point $50 \ m$ away from the base of a multistoreyed building,the angle of elevation of the first floor is found to be $30^{\circ}$ and the angle of elevation of the fifteenth floor is found to be $60^{\circ}$. What is the distance between the first floor and the fifteenth floor? (in $m$)

When observed from the top of a tower,the angles of depression of two houses $A$ and $B$ in the Eastern and Western directions are $30^{\circ}$ and $60^{\circ}$ respectively. Then........

The angle of elevation of the top of tower $N$ from the base of tower $M$ is $40^{\circ}$. The angle of elevation of the top of tower $M$ from the base of tower $N$ is $55^{\circ}$. Then,.......

$A$ $15\ m$ high eucalyptus tree standing erect on the ground breaks at the height of $5\ m$ from the ground. The broken part bends such that the top of the tree touches the ground. Find the angle made by the broken part of the tree with the ground. (in $^{\circ}$)