If the angles of elevation of the top of a tower from three collinear points $A, B$ and $C$ on a line leading to the foot of the tower are $30^o, 45^o$ and $60^o$ respectively,then the ratio $AB : BC$ is:

The angular elevation of a tower $CD$ at a point $A$ due south of it is $60^\circ$ and at a point $B$ due west of $A$,the elevation is $30^\circ$. If $AB = 3 \, km$,the height of the tower 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 $... \ m$.

Two parallel towers $A$ and $B$ of different heights are at some distance $d$ on the same level ground. If the angle of elevation of a point $P$ at $20\,m$ height on tower $B$ from a point $Q$ at $10\,m$ height on tower $A$ is $\theta$,and this angle is equal to half the angle of elevation of point $R$ at $50\,m$ height on tower $A$ from point $P$ on tower $B$,then $\theta$ is equal to....$^o$

$A$ vertical pole of height $h$ stands on a building of height $H$. The angle of elevation of the top of the building from a point on the ground,which is $5$ units away from the foot of the building,is $\alpha$. The pole subtends an angle $\beta$ at the same point on the ground. If $2 \tan \beta \cot \alpha = 1$,then-

If the angle of elevation of the top of a tower at a distance of $500 \, m$ from its foot is $30^\circ$,then the height of the tower is: