Watching from a point on the ground $20 \, m$ away from the base of an erect pole,the angle of elevation of the top of the pole is found to be $45^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

$A$ pole stands on the ground. Watching from the top of the pole,the angle of depression of a stone on the ground $10 \, m$ away from the pole is $60^{\circ}$. Then the height of the pole is $\ldots \ldots \ldots \, m$. (Take $\sqrt{3} = 1.73$.)

Write 'True' or 'False' and justify your answer.
If the length of the shadow of a tower is increasing,then the angle of elevation of the sun is also increasing.

In a right triangle,if the length of the hypotenuse is $12$ and the measure of one of the angles is $30^{\circ}$,then the measure of the side opposite to the angle is $\ldots \ldots \ldots \ldots$

In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $m \angle C = \theta$,then $\tan \theta = \dots$

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 $m$)