The height of a tower is $60 \, m$. From a point on the ground,the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the distance of that point from the base of the tower. (in $m$)

Observing from the top of a tower,the angle of depression of an object $30 \ m$ away from the base of the tower is found to be $45^\circ$. Find the height of the tower (in $m$).

The shadow of a tower standing on a level plane is found to be $50 \, m$ longer when the Sun's elevation is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower (in $m$).

In $\Delta ABC$,$m\angle B = 90^\circ$,$m\angle C = 30^\circ$ and $AC = 30 \text{ cm}$,then $AB = \ldots \text{ cm}$.

From a point $50 \ m$ away from the base of a multistoreyed building,the angle of elevation of the first floor is found to be $30^{\circ}$ and the angle of elevation of the fifteenth floor is found to be $60^{\circ}$. What is the distance between the first floor and the fifteenth floor? (in $m$)

The height of a tower is $50 \, m$ and the height of a building is $30 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the tower is $\alpha$ and that of the building is $\beta$. Then,which of the following holds true?