The angle of elevation of the top of a tower from a point $20\, m$ away from the base of the tower is found to be $30^{\circ}$. Find the height of the tower. (in $, m$)

From the top of a $7 \,m$ high building,the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$. Determine the height of the tower.

$A$ tower stands vertically on the ground. The angle of elevation of the top of the tower from a point $100 \, m$ away from the base of the tower is $60^\circ$. The height of the tower is $\ldots \ldots \ldots \ldots \, m$.

$A$ cable tied to the top of an electric pole is fixed at a point on the ground. The length of the cable is $20 \, m$. If it makes an angle of $30^{\circ}$ with the ground,then the height of the electric pole is ........ (in $, m$)

$A$ ladder leans against a wall. It makes an angle of $45^{\circ}$ with the ground and reaches a height of $10 \, m$ on the wall. Find the length of the ladder and the distance between the lower end of the ladder and the base of the wall.

The height of a building is $11 \, m$ and the height of a pole is $8 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the pole is $\alpha$ and that of the top of the building is $\beta$. Then,$\ldots \ldots \ldots$ holds true.