$A$ cable tied to the top of an electric pole is fixed at a point on the ground. The length of the cable is $22\, m$ and it makes an angle of measure $30^{\circ}$ with the ground. Find the height of the electric pole (in $m$).

There is a flag-post on the top of a $10 \, m$ high tower. From a point on the ground,the angle of elevation of the top of the tower is $45^{\circ}$ and that of the top of the flag-post is $60^{\circ}$. Find the height of the flag-post. (in $, m$)

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 $\ldots \ldots \ldots \ m$.

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

In a right triangle,if the measure of one of the angles is $45^{\circ}$,then the measure of the side opposite to the angle with measure $45^{\circ}$ is $\ldots \ldots \ldots$ times the measure of the hypotenuse.

Write 'True' or 'False' and justify your answer.
$\tan \theta$ increases faster than $\sin \theta$ as $\theta$ increases for $0^\circ < \theta < 90^\circ$.