The angle of depression of a car parked on the road as observed from the top of a building is $60^{\circ}$. The angle of depression of that car from a window $14.6 \, m$ below the top is $45^{\circ}$. Find the distance between the car and the building (in $m$).

$A$ pole stands vertically on the ground. The length of the shadow of the pole is $\frac{1}{\sqrt{3}}$ times the height of the pole. Then,the angle of elevation of the sun is $\ldots \ldots \ldots \ldots . . .$ (in $^\circ$)

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

From a point $A$ on the ground,the angle of elevation of the top of a tower is found to be $45^{\circ}$. If the distance between point $A$ and the base of the tower is $x$ and the height of the tower is $y$,then which of the following holds true?

The angle of elevation of building $Y$ from the bottom of building $X$ is $45^{\circ}$ and the angle of elevation of building $X$ from the bottom of building $Y$ is $65^{\circ}.$ Then:

From a point $50 \ m$ away from the base of a multistoreyed building,the angle of elevation of the first floor is found to be $30^{\circ}$ and the angle of elevation of the fifteenth floor is found to be $60^{\circ}$. What is the distance between the first floor and the fifteenth floor? (in $m$)