$A$ man whose eye level is $1.5 \ m$ above the ground observes the angle of elevation of a tower to be $60^\circ$. If the distance of the man from the tower is $10 \ m$,the height of the tower is:

$A$ tower $T_1$ of height $60 \, m$ is located exactly opposite to a tower $T_2$ of height $80 \, m$ on a straight road. From the top of $T_1$,if the angle of depression of the foot of $T_2$ is twice the angle of elevation of the top of $T_2$,then the width (in $m$) of the road between the feet of the towers $T_1$ and $T_2$ is

If the angles of elevation of two towers from the middle point of the line joining their feet are $60^\circ$ and $30^\circ$ respectively,then the ratio of their heights is

The angle of elevation of a cloud $C$ from a point $P$,$200 \ m$ above a still lake is $30^{\circ}$. If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ}$,then $PC$ (in $m$) is equal to

$A$ tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB = a$ subtends an angle of $60^{\circ}$ at the foot of the tower,and the angle of elevation of the top of the tower from $A$ or $B$ is $30^{\circ}$. The height of the tower is

From the top of a lighthouse $30 \ m$ high with its base at sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is: