An aeroplane flying at a constant speed,parallel to the horizontal ground,$\sqrt{3} \ km$ above it,is observed at an elevation of $60^\circ$ from a point on the ground. If,after five seconds,its elevation from the same point is $30^\circ$,then the speed (in $km/hr$) of the aeroplane is

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

The angle of elevation of the sun,when the shadow of the pole is $\sqrt{3}$ times the height of the pole,is ....$^o$

If a flag-staff of $6 \ m$ high placed on the top of a tower throws a shadow of $2 \sqrt{3} \ m$ along the ground,then the angle (in degrees) that the sun makes with the ground is.....$^o$

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

$A$ balloon is observed simultaneously from three points $A, B$ and $C$ on a straight road directly under it. The angular elevation at $B$ is twice and at $C$ is thrice that of $A$. If the distance between $A$ and $B$ is $200$ metres and the distance between $B$ and $C$ is $100$ metres,then the height of the balloon is: