The angle of elevation of the top of a pole from a point $x \, m$ away from the base of the pole is $60^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

$A$ ladder is leaning against a wall such that its upper end touches the wall at a height of $3 \, m$ and the ladder is inclined at an angle of $30^{\circ}$ with the ground. Find the length of the ladder in $m$.

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 $\ldots \ldots \ldots \, m$.

The approximate value of $\sqrt{3}$ up to $2$ decimal places is $\ldots \ldots \ldots$

Observing an object from the point of observation,if one gets the angle of depression,then the object under observation is $\ldots \ldots \ldots . . .$

$A$ cable tied to the top of an electric pole is affixed at a point on the ground $a \text{ m}$ away from the pole. If the cable makes an angle $\theta$ with the ground,then prove that the height of the pole is $a \tan \theta \text{ m}$ and the length of the wire is $a \sec \theta \text{ m}$.