The angle of elevation of the top of a tower from a point on the ground,which is $30\, m$ away from the foot of the tower,is $30^{\circ}$. Find the height of the tower.

An electrician has to repair an electric fault on a pole of height $5\, m$. She needs to reach a point $1.3\, m$ below the top of the pole to undertake the repair work (see figure). What should be the length of the ladder that she should use which,when inclined at an angle of $60^{\circ}$ to the horizontal,would enable her to reach the required position? Also,how far from the foot of the pole should she place the foot of the ladder? (You may take $\sqrt{3}=1.73$)

From a point on a bridge across a river,the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$,respectively. If the bridge is at a height of $3 \, m$ from the banks,find the width of the river.

The angles of depression of the top and the bottom of an $8 \, m$ tall building from the top of a multi-storeyed building are $30^{\circ}$ and $45^{\circ}$,respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

$A$ straight highway leads to the foot of a tower. $A$ man standing at the top of the tower observes a car at an angle of depression of $30^{\circ}$,which is approaching the foot of the tower with a uniform speed. Six seconds later,the angle of depression of the car is found to be $60^{\circ}$. Find the time taken by the car to reach the foot of the tower from this point (in $seconds$).

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.