On walking for search of a ball $x$ metres on a hill making an angle of $30^{\circ}$ with the ground,one can reach a height of $y$ metres from the ground. Then $\ldots \ldots \ldots . . .$

Watching from a point $A$ on the ground $x \ m$ away from the base of the building. The height of the building is $y$ and the angle of elevation of the top of the building is found to be $25^\circ$. Then,$\ldots \ldots \ldots \ldots .$

Observing from the top of a tower,the angles of depression of the top and the bottom of a $100 \, m$ high building are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower in $m$.

From the top of a $50 \, m$ high tower,the angle of depression of a parked car is found to be $30^\circ$. Find the distance between the car and the base of the tower. (in $m$)

$A$ $10\,m$ long ladder is placed in such a manner that its lower end remains $5\,m$ away from the base of a wall. Find the angles made by the ladder with the wall and with the floor.

The angle of elevation of a cloud from a point $h$ metres above the surface of a lake is $\theta$ and the angle of depression of its reflection in the lake is $\phi$. Prove that the height of the cloud above the lake is $h\left(\frac{\tan \phi+\tan \theta}{\tan \phi-\tan \theta}\right).$