Watching from a point on the ground $20 \, m$ away from the base of an erect pole,the angle of elevation of the top of the pole is found to be $45^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

The height of a tower is $30 \ m$. Find the length of the shadow of the tower,when the angle of elevation of the sun is $45^\circ$. (in $m$)

Two cars are parked in the same direction of a tower. Observing from the top of the tower,their angles of depression are found to be $60^{\circ}$ and $30^{\circ}$. If the car nearer to the tower is $75\, m$ away from the tower,find the distance between these two cars (in $m$).

Watching from the top of a building and from a window $10 \, m$ below the top,the angles of depression of a car on the ground are found to be $60^{\circ}$ and $45^{\circ}$ respectively. Find the distance of the car from the building. (in $m$)

Two ships are anchored in the opposite directions from a lighthouse. The angle of depression of one ship from the top of the lighthouse is $60^{\circ}$ and that of the other ship from the same place is found to be $30^{\circ}$. If the ship with the angle of depression of $60^{\circ}$ is $150\,m$ away from the lighthouse,find the distance between these two ships (in $m$).

$A$ pole $6\, m$ high casts a shadow $2 \sqrt{3}\, m$ long on the ground. Then,the Sun's elevation is: (in $^{\circ}$)