The angle of elevation of the top of the tower from a point $x \, m$ away from the tower is $30^{\circ}$. Then the height of the tower is $\ldots \ldots \ldots \, m$.

Observing from the top of a tower,the angles of depression of the top and the bottom of a $100 \, m$ high building are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower in $m$.

$A$ circus artist is climbing a $20\, m$ long rope,which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole,if the angle made by the rope with the ground level is $30^{\circ}$ (see figure). (in $m$)

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 $m$)

The lower window of a house is at a height of $2\, m$ above the ground and its upper window is $4\, m$ vertically above the lower window. At a certain instant,the angles of elevation of a balloon from these windows are observed to be $60^{\circ}$ and $30^{\circ}$,respectively. Find the height of the balloon above the ground (in $m$).

$A$ boat is sailing with constant speed towards a man sitting on a tree on the river bank. At some moment,the man measures the angle of depression of the boat as $30^{\circ}$. $10$ minutes later,this angle is measured as $60^{\circ}$. How much longer will the boat now take to reach the bank? (in $min$)