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,.......

$A$ cable tied to the top of an electric pole is fixed at a point on the ground. The length of the cable is $20 \, m$. If it makes an angle of $30^{\circ}$ with the ground,then the height of the electric pole is ........ (in $, m$)

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 $, m$)

$A$ straight highway leads to the foot of a tower. $A$ man standing at the top of the tower observes a car at an angle of depression of $30^{\circ}$,which is approaching the foot of the tower with a uniform speed. Six seconds later,the angle of depression of the car is found to be $60^{\circ}$. Find the time taken by the car to reach the foot of the tower from this point (in $seconds$).

From a point $h$ metres above the water level of a lake,the angle of elevation of the top of a palace is found to be $\alpha$ and the angle of depression of the image of the top of the palace observed in the lake is found to be $\beta$. Find the height of the palace.

Watching from the top of a tower,the angles of depression of two houses $A$ and $B$ are found to be $25^{\circ}$ and $40^{\circ}$ respectively. Then,.......