$A$ person is watching from a point $A$ on the ground,which is $x \ m$ away from the base of a building. The height of the building is $y \ m$ and the angle of elevation of the top of the building is found to be $70^\circ$. Then:

Observing from the top of a tower,the angles of depression of the top and the bottom of a $100 \, m$ high building are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower in $m$.

In a right triangle,if the measure of one of the angles is $30^{\circ}$,then the side opposite to the angle with measure $30^{\circ}$ is .......... times the hypotenuse.

$A$ 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 $a \sec \theta \text{ m}$.

$A$ ladder leans on a wall to reach a height of $3 \, m$ on the wall. If the ladder makes an angle of $30^{\circ}$ with the ground,the length of the ladder is ........... $m$.

From the top of a building $h$ metres high,the angle of depression of an object on the ground is $\theta$. The distance (in metres) of the object from the foot of the building is $\ldots \ldots \ldots$