$A$ flag-post $20 \ m$ high standing on the top of a house subtends an angle whose tangent is $\frac{1}{6}$ at a distance $70 \ m$ from the foot of the house. The height of the house is......$m$

$A$ tower subtends an angle $\alpha$ at a point $A$ in the plane of its base,and the angle of depression of the foot of the tower from a point $P$ at a height $l$ meters vertically above $A$ is $\beta$. The height of the tower is

The shadow of a tower standing on a level ground is found to be $60 \ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is

The horizontal distance between two towers is $60 \ m$. The angle of depression of the top of the first tower as seen from the top of the second tower is $30^\circ$. If the height of the second tower is $150 \ m$,then the height of the first tower is:

From a point on the level ground, the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole, the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is:

Let a vertical tower $AB$ of height $2h$ stand on a horizontal ground. From a point $P$ on the ground,a man can see up to height $h$ of the tower with an angle of elevation $2\alpha$. When he moves a distance $d$ from $P$ in the direction of $\overline{AP}$,he can see the top $B$ of the tower with an angle of elevation $\alpha$. If $d=\sqrt{7}h$,then $\tan \alpha$ is equal to: