If the angle of depression of a point $A$ on the ground from the top of a tower is $30^\circ$,then the angle of elevation of the top of the tower from the point $A$ will be .............. $^\circ $.

The angle of elevation of a tower from point $P$ due north of it is $30^\circ$ and from a point $Q$ due east of point $P$ is $\theta$. If the distance of the foot of the tower from point $P$ is $3 \ m$ and $PQ = 3 \ m$,then $\theta$ is equal to-

From the top of a lighthouse $60 \ m$ high with its base at the sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

From a $60 \ m$ high tower,the angles of depression of the top and bottom of a house are $\alpha$ and $\beta$ respectively. If the height of the house is $\frac{60 \sin(\beta - \alpha)}{x}$,then $x =$

From the bottom of a pole of height $h,$ the angle of elevation of the top of a tower is $\alpha$ and the pole subtends an angle $\beta$ at the top of the tower. The height of the tower 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: