$A$ 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 $seconds$).

From a point on the ground,the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20 \, m$ high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.

The shadow of a tower standing on a level ground is found to be $40 \, m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $60^{\circ} .$ 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 $\sqrt{3}=1.73$)

$A$ circus artist is climbing a $20\, m$ long rope,which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole,if the angle made by the rope with the ground level is $30^{\circ}$ (see figure). (in $m$)

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.