From the top of a $50 \, m$ high tower,the angle of depression of a parked car is found to be $30^\circ$. Find the distance between the car and the base of the tower. (in $m$)

On walking for search of a ball $x$ metres on a hill making an angle of $30^{\circ}$ with the ground,one can reach a height of $y$ metres from the ground. Then $\ldots \ldots \ldots . . .$

The height of a tower is $50 \, m$ and the height of a building is $30 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the tower is $\alpha$ and that of the building is $\beta$. Then,which of the following holds true?

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

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

$A$ spherical balloon of radius $r$ subtends an angle $\theta$ at the eye of an observer. If the angle of elevation of its centre is $\phi$,find the height of the centre of the balloon.