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

When observed from the top of a tower,the angles of depression of two houses $A$ and $B$ in the Eastern and Western directions are $30^{\circ}$ and $60^{\circ}$ respectively. Then........

From the top of a hill $100 \, m$ high,the angles of depression of the top and the bottom of a tower are observed to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the height of the tower in meters.

An observer $1.5 \ m$ tall is $20.5 \ m$ away from a tower $22 \ m$ high. Determine the angle of elevation of the top of the tower from the eye of the observer. (in $^{\circ}$)

As observed from a hill $340 \ m$ high,the angles of depression of two houses situated to the east and west of the hill are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the distance between the two houses. (in $m$)

There is a $100\, m$ high tower at some distance from a cliff. The angle of elevation of the top of the cliff from the base of the tower is $45^{\circ}$ and the angle of depression of the base of the cliff from the top of the tower is $30^{\circ}$. Find the height of the cliff and also the distance between the tower and the cliff.