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

Watching from the top of an $80 \, m$ high hill,the angle of elevation of the top of a tower is $30^\circ$ and the angle of depression of the base of the tower is $45^\circ$. Find the height of the tower in $m$.

When the angle of elevation of the sun increases from $30^{\circ}$ to $60^{\circ},$ the shadow of a tower decreases by $50\, m .$ Find the height of the tower in $m$.

The angle of depression of the base of a tower from the top of a cliff is $60^{\circ}$ and the angle of elevation of the top of the tower from the base of the cliff is $30^{\circ}$. If the height of the tower is $50 \, m$,find the height of the cliff in meters.

The angle of elevation of the top of tower $N$ from the base of tower $M$ is $40^{\circ}$. The angle of elevation of the top of tower $M$ from the base of tower $N$ is $55^{\circ}$. Then,.......

As observed from the top of a tower $30 \, m$ high,the angle of depression of a stone on the ground is found to be $45^{\circ}$. Find the distance between the stone and the tower (in $m$).