The angle of depression of a stone from the top of a tower is $45^{\circ}$ and the height of the tower is $30 \, m$. Then the distance between the tower and the stone is ......... $m$.

Two cars are parked in the same direction of a tower. Observing from the top of the tower,their angles of depression are found to be $60^{\circ}$ and $30^{\circ}$. If the car nearer to the tower is $75\, m$ away from the tower,find the distance between these two cars (in $m$).

From the top of a building $h \ m$ high,the angle of elevation of the top of a pole is found to be $\alpha$,while the angle of depression of the base of the pole is found to be $\beta$. Prove that the height of the pole is $h(1 + \tan \alpha \cdot \cot \beta) \ m$.

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

The height of a lighthouse is $100\, m$. Two boats are anchored in the opposite directions from the lighthouse. The angle of depression of each boat from the top of the lighthouse is found to be $30^\circ$. Find the distance between these two boats (in $m$).

$A$ ladder leans against a wall. It makes an angle of $45^{\circ}$ with the ground and reaches a height of $10 \, m$ on the wall. Find the length of the ladder and the distance between the lower end of the ladder and the base of the wall.