Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as $45^{\circ}$ and $30^{\circ}$ respectively. If the height of the tower is $40 \, m,$ find the distance between the men.

$A$ flag-staff of $5 \, m$ high stands on a building of $25 \, m$ high. An observer is at a height of $30 \, m$. The flag-staff and the building subtend equal angles at the observer. The distance of the observer from the top of the flag-staff is

The angle of elevation of a point situated at a distance of $70 \ m$ from the base of a tower is $45^\circ$. The height of the tower is ..... $m$.

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

$A$ bird is sitting on the top of a vertical pole $20 \ m$ high and its angle of elevation from a point $O$ on the ground is $45^o$. It flies off horizontally straight away from the point $O$. After one second,the angle of elevation of the bird from $O$ is reduced to $30^o$. Then the speed (in $m/s$) of the bird is

An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be $30^\circ$. After $3 \text{ minutes}$,this angle becomes $60^\circ$. After how much more time will the car reach the tree? (in minutes)