Watching from the top of a $30 \ m$ high tower,the angle of depression of a stone on the ground is found to be $45^{\circ}$. Then the distance of the stone from the base of the tower is $\ldots \ldots \ldots \ m$.

$A$ flag-staff stands on the top of a building. The angle of elevation of the top of the building is $45^{\circ}$ and that of the top of the flag-staff is $60^{\circ}$,as observed by a man standing $15\, m$ away from the building. Find the height of the flag-staff from the top of the building (in $m$).

The angle of depression of a stone from the top of a tower is $45^{\circ}$ and the height of the tower is $30 \, m$. Then the distance between the tower and the stone is ......... $m$.

Write 'True' or 'False' and justify your answer.
The value of $\tan \theta$ (where $\theta < 90^{\circ}$) increases as $\theta$ increases.

An observer $1.5\, m$ tall is $28.5\, m$ away from a tower. The angle of elevation of the top of the tower from his eyes is $45^\circ$. Then the height of the tower is ............ $m$.

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.