The angle of elevation of a stationary cloud from a point $2500 \, m$ above a lake is $15^\circ$ and the angle of depression of its reflection in the lake is $45^\circ$. The height of the cloud above the lake level is

$A$ vertical pole fixed to the horizontal ground is divided in the ratio $3:7$ by a mark on it,with the lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground $18 \ m$ away from the base of the pole,then the height of the pole (in $meters$) is:

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 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 $... \ m$.

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:

The angle of elevation of the top $P$ of a tower from the feet of one person standing due South of the tower is $45^{\circ}$ and from the feet of another person standing due West of the tower is $30^{\circ}$. If the height of the tower is $5 \text{ m}$,then the distance (in meters) between the two persons is equal to $..........$.