$A$ pole stands slanting on the ground making an angle of $60^{\circ}$ with the ground. At high noon,the length of the shadow of the pole is $3 \, m$. Find the length of the pole in $m$.

$A$ $1.5 \, m$ tall boy is standing at some distance from a $30 \, m$ tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ}$ to $60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.

$A$ $15\ m$ high eucalyptus tree standing erect on the ground breaks at the height of $5\ m$ from the ground. The broken part bends such that the top of the tree touches the ground. Find the angle made by the broken part of the tree with the ground. (in $^{\circ}$)

$A$ tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground,making an angle of $30^{\circ}$ with it. The distance between the foot of the tree and the point where the top touches the ground is $8\, m$. Find the height of the tree.

From a point on the ground,the angle of elevation of the top of a tower is found to be $30^{\circ}$. Walking $30\, m$ towards the tower from that point,the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the height of the tower (in $m$).

$A$ tower stands vertically on the ground. From a point on the ground,which is $15\, m$ away from the foot of the tower,the angle of elevation of the top of the tower is found to be $60^{\circ}.$ Find the height of the tower. (in $m$)