$A$ ladder leans on a wall to reach a height of $3 \, m$ on the wall. If the ladder makes an angle of $30^{\circ}$ with the ground,the length of the ladder is ........... $m$.

The angle of depression of a stone from the top of a tower is $45^{\circ}$ and the height of the tower is $30 \, m$. Then the distance between the tower and the stone is ......... $m$.

$A$ person is watching from a point $A$ on the ground,which is $x \ m$ away from the base of a building. The height of the building is $y \ m$ and the angle of elevation of the top of the building is found to be $70^\circ$. Then:

The angle of elevation of the top of a hill from a point on the ground is $30^\circ$. After walking $30 \, m$ towards the hill,the angle of elevation becomes $45^\circ$. What is the height of the hill? (in $m$)

The angles of depression of two cars parked in the same direction of a $50\, m$ high tower are found to be $30^{\circ}$ and $60^{\circ}$. Find the distance between these two cars. (in $, m$)

The shadow of a tower standing on a level plane is found to be $50 \, m$ longer when the Sun's elevation is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower (in $m$).