The angle of elevation of a jet plane from a point $A$ on the ground is $60^{\circ}$. After a flight of $20 \, s$ at the speed of $432 \, km/h$, the angle of elevation changes to $30^{\circ}$. If the jet plane is flying at a constant height, then its height is ..... $m$. (in $\sqrt{3}$)

The sum of angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then, the height of the tower is

$A$ house subtends a right angle at the window of an opposite house. The angle of elevation of the window from the bottom of the first house is $30^{\circ}$. If the distance between the two houses is $6 \ m$,then the height of the first house is:

The angle of elevation of the top of a vertical tower from a point $P$ on the horizontal ground was observed to be $\alpha$. After moving a distance $2 \ m$ from $P$ towards the foot of the tower,the angle of elevation changes to $\beta$. Then the height (in metres) of the tower is

$A$ person observes the top of a tower from a point $A$ on the ground. The angle of elevation of the tower from this point is $60^{\circ}$. He moves $60 \ m$ in the direction perpendicular to the line joining $A$ and the base of the tower to reach point $C$. The angle of elevation of the tower from point $C$ is $45^{\circ}$. Then, the height of the tower (in metres) is

Two vertical poles are $150 \ m$ apart and the height of one is three times that of the other. If from the middle point of the line joining their feet,an observer finds the angles of elevation of their tops to be complementary,then the height of the shorter pole (in meters) is