The angle of elevation of the top of a pole from a point $x \, m$ away from the base of the pole is $60^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

$A$ tree stands vertically on the bank of a river. The angle of elevation of the top of the tree from a point exactly opposite to the tree on the other bank of the river is $60^{\circ}$. The angle of elevation of the top of the tree from a point $40 \ m$ away from that point is $30^{\circ}$. Find the width of the river and the height of the tree.

The approximate value of $\frac{1}{\sqrt{3}}$ up to $2$ decimal places is.........

Two boats are anchored in the same direction from a $100 \, m$ high lighthouse. The angles of depression of the boats from the top of the lighthouse are $30^{\circ}$ and $45^{\circ}$. Find the distance between these two boats (in $m$).

In a right triangle,if the measure of one of the angles is $60^{\circ}$,then the measure of the side opposite to the angle with measure $60^{\circ}$ is $\ldots \ldots$ times the measure of the hypotenuse.

$A$ $1.2 \, m$ tall girl spots a balloon moving with the wind in a horizontal line at a height of $88.2 \, m$ from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$. After some time,the angle of elevation reduces to $30^{\circ}$. Find the distance travelled by the balloon during this interval.