$A$ tower subtends an angle of $30^\circ$ at a point distant $d$ from the foot of the tower and on the same level as the foot of the tower. At a second point $h$ vertically above the first,the angle of depression of the foot of the tower is $60^\circ$. The height of the tower is:

From the top of a hill $h$ metres high, the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

The angle of elevation of the top of a pillar at a point $A$ on the ground is $15^\circ$. On walking $40 \ m$ towards the pillar,the angle becomes $30^\circ$. The height of the pillar is $... \ m$.

The angle of elevation of the summit of a mountain from a point on the ground is $45^{\circ}$. After climbing up $1 \ km$ towards the summit at an inclination of $30^{\circ}$ from the ground,the angle of elevation of the summit is found to be $60^{\circ}$. Then the height (in $km$) of the summit from the ground is

The tops of two poles of height $20 \ m$ and $14 \ m$ are connected by a wire. If the wire makes an angle $30^{\circ}$ with the horizontal,then the length of the wire is $... \ m$.

Consider a triangular plot $ABC$ with sides $AB = 7 \ m$,$BC = 5 \ m$,and $CA = 6 \ m$. $A$ vertical lamp-post at the midpoint $D$ of $AC$ subtends an angle $30^o$ at $B$. The height (in $m$) of the lamp-post is