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 top of a vertical tower standing on a horizontal plane is observed to be $45^o$ from a point $A$ on the plane. Let $B$ be a point $30 \, m$ vertically above the point $A$. If the angle of elevation of the top of the tower from $B$ is $30^o$,then the distance (in $m$) of the foot of the tower from the point $A$ is:

$A$ person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is $45^\circ$. Which of the following statements is correct?

The base of a cliff is circular. From the extremities of a diameter of the base,the angles of elevation of the top of the cliff are $30^\circ$ and $60^\circ$. If the height of the cliff is $500 \ m$,then the diameter of the base of the cliff is:

The angle of elevation of the top of the tower observed from each of the three points $A, B, C$ on the ground,forming a triangle,is the same angle $\alpha$. If $R$ is the circum-radius of the $\Delta ABC$,then the height of the tower is