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

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

Observing an object from the point of observation,if one gets the angle of depression,then the object under observation is $\ldots \ldots \ldots . . .$

From a point $h$ metres above the water level of a lake,the angle of elevation of the top of a palace is found to be $\alpha$ and the angle of depression of the image of the top of the palace observed in the lake is found to be $\beta$. Find the height of the palace.

Observing from the top of a $150\, m$ high tower,the angle of depression of a cycle on the ground is found to be $60^{\circ}$. How far away is the cycle from the tower?

The height of a tower is $60 \, m$. From a point on the ground,the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the distance of that point from the base of the tower. (in $m$)