The shadow of a tower standing on a level plane is found to be $100 \ m$ longer when the sun's angle of elevation is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is:

The angle of elevation of the top of a tower at a point on the ground is $30^\circ$. If on walking $20 \, m$ toward the tower,the angle of elevation becomes $60^\circ$,then the height of the tower is:

The angle of elevation of the top of a tower from a point $A$ due south of the tower is $\alpha$ and from a point $B$ due east of the tower is $\beta$. If $AB = d$,then the height of the tower is

From the top of a lighthouse $30 \ m$ high with its base at sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

If the angle of elevation of a cloud from a point $P$ which is $25 \, m$ above a lake is $30^o$ and the angle of depression of the reflection of the cloud in the lake from $P$ is $60^o$,then the height of the cloud (in meters) from the surface of the lake 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: