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.

If the angle of elevation of the top of a tower at a distance of $500 \, m$ from its foot is $30^\circ$,then the height of the tower is:

$AB$ is a vertical pole with $B$ at the ground level and $A$ at the top. $A$ man finds that the angle of elevation of the point $A$ from a certain point $C$ on the ground is $60^{\circ}$. He moves away from the pole along the line $BC$ to a point $D$ such that $CD = 7 \ m$. From $D$,the angle of elevation of the point $A$ is $45^{\circ}$. Then the height of the pole is

The angle of elevation of a cloud $C$ from a point $P$,$200 \ m$ above a still lake is $30^{\circ}$. If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ}$,then $PC$ (in $m$) is equal to

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)

The shadow of a tower of height $(1 + \sqrt{3}) \text{ m}$ standing on the ground is found to be $2 \text{ m}$ longer when the sun's elevation is $30^{\circ}$ than when the sun's elevation was $...^{\circ}$.