$A$ 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 $m$)

$A$ kite is flying at a height of $60\, m$ above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$. Find the length of the string,assuming that there is no slack in the string.

Two poles of equal heights are standing opposite each other on either side of the road,which is $80\, m$ wide. From a point between them on the road,the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ},$ respectively. Find the height of the poles and the distances of the point from the poles.

As observed from the top of a $75 \, m$ high lighthouse from the sea-level,the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$. If one ship is exactly behind the other on the same side of the lighthouse,find the distance between the two ships.

$A$ $1.2\, m$ 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 $30^{\circ}$ (see $Fig.$). Find the distance travelled by the balloon during the interval.

The shadow of a tower standing on a level ground is found to be $40 \, m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $60^{\circ} .$ Find the height of the tower.