The angles of elevation of the top of a tower from three collinear points $A, B$,and $C$ on a road leading to the foot of the tower are $30^{\circ}, 45^{\circ}$,and $60^{\circ}$ respectively. The ratio of $AB$ to $BC$ is

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

$A$ man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes $18 \text{ min}$ for the angle of depression of the car to change from $30^\circ$ to $45^\circ$,then after this,the time taken (in min) by the car to reach the foot of the tower is:

The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base to be $30^{\circ}$. After walking $120 \ m$ towards it on level ground,the angle of elevation is found to be $60^{\circ}$. Then the height of the object (in metres) is:

The angle of elevation of a point situated at a distance of $70 \ m$ from the base of a tower is $45^\circ$. The height of the tower is ..... $m$.

$A$ $20 \ m$ long tree is broken by the wind such that its top touches the ground at an angle of $30^\circ$. The height from the ground at which the tree is broken is: