The angle of elevation of the top of the tower observed from each of the three points $A, B, C$ on the ground,forming a triangle,is the same angle $\alpha$. If $R$ is the circum-radius of the $\Delta ABC$,then the height of the tower is

$A$ flag-staff of $5 \, m$ high stands on a building of $25 \, m$ high. An observer is at a height of $30 \, m$. The flag-staff and the building subtend equal angles at the observer. The distance of the observer from the top of the flag-staff is

The angles of elevation of the top of a tower $A$ from the top $B$ and bottom $D$ of a building of height $a$ are $30^\circ$ and $45^\circ$ respectively. If the tower and the building stand at the same level,then 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:

An observer in a boat finds that the angle of elevation of the top of a tower standing on the top of a cliff is $60^\circ$ and that of the top of the cliff is $30^\circ$. If the height of the tower is $60 \ m$,then the height of the cliff is ... $m$.

Two pillars of equal height stand on either side of a roadway which is $60 \, m$ wide. At a point in the roadway between the pillars,the angles of elevation of the top of the pillars are $60^\circ$ and $30^\circ$. The height of the pillars is