The angle of elevation of the top of a pole from a point $x \, m$ away from the base of the pole is $60^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

From the top of a building $h \ m$ high,the angle of elevation of the top of a pole is found to be $\alpha$,while the angle of depression of the base of the pole is found to be $\beta$. Prove that the height of the pole is $h(1 + \tan \alpha \cdot \cot \beta) \ m$.

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,$\ldots \ldots \ldots \ldots .$

$A$ 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 $seconds$).

The angles of depression of two boats $A$ and $B$ from the top of a lighthouse are $25^{\circ}$ and $40^{\circ}$ respectively. Then $\ldots \ldots \ldots \ldots$ from the lighthouse.

From a point on the ground,the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20 \, m$ high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.