$A$ circus artist is climbing a $20\, m$ long rope,which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole,if the angle made by the rope with the ground level is $30^{\circ}$ (see figure). (in $m$)

From a point $A$,$h \text{ m}$ above the ground level,the angle of elevation of the top of a tower is $\alpha$ and the angle of depression of the base of the tower is $\beta$. Prove that the height of the tower is $\frac{h(\tan \alpha + \tan \beta)}{\tan \beta} \text{ m}$.

The angle of depression of the top of a building from the top of a tower is $45^{\circ}$ and that of the base of the building from the top of the tower is $60^{\circ}$. If the height of the building is $7 \, m$,find the height of the tower.

Watching from the top of a building and from a window $10 \, m$ below the top,the angles of depression of a car on the ground are found to be $60^{\circ}$ and $45^{\circ}$ respectively. Find the distance of the car from the building. (in $m$)

As observed from the top of a building,the angle of depression of a man standing $10 \, m$ away from the building is found to be $45^{\circ}$. Find the height of the building (in $m$).

Observing from the top of a building,the angle of elevation of the top of a tower is $30^{\circ}$ and the angle of depression of the base of the tower is $60^{\circ}$. If the height of the building is $36 \, m$,find the height of the tower (in $m$).