An observer $1.5\, m$ tall is $28.5\, m$ away from a tower. The angle of elevation of the top of the tower from his eyes is $45^\circ$. Then the height of the tower is ............ $m$.

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 $m$).

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 ......... $m$.

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 $m$).

From the top of a tower,the angles of depression of two vehicles on the same side of the tower are found to be $\alpha$ and $\beta$ $(\alpha > \beta)$. If the distance between the vehicles is $b$,show that the height of the tower is $\frac{b \tan \alpha \tan \beta}{\tan \alpha - \tan \beta}$.

There is a $100\, m$ high tower at some distance from a cliff. The angle of elevation of the top of the cliff from the base of the tower is $45^{\circ}$ and the angle of depression of the base of the cliff from the top of the tower is $30^{\circ}$. Find the height of the cliff and also the distance between the tower and the cliff.