$A$ person is standing on a tower of height $15(\sqrt{3} + 1) \ m$ and observing a car coming towards the tower. He observes that the angle of depression changes from $30^\circ$ to $45^\circ$ in $3 \ s$. What is the speed of the car in $km/hr$?

$A$ 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

The angle of elevation of the summit of a mountain from a point on the ground is $45^{\circ}$. After climbing up $1 \ km$ towards the summit at an inclination of $30^{\circ}$ from the ground,the angle of elevation of the summit is found to be $60^{\circ}$. Then the height (in $km$) of the summit from the ground is

The angle of elevation of the top $P$ of a vertical tower $PQ$ of height $10$ from a point $A$ on the horizontal ground is $45^{\circ}$. Let $R$ be a point on $AQ$ and from a point $B$,vertically above $R$,the angle of elevation of $P$ is $60^{\circ}$. If $\angle BAQ = 30^{\circ}$,$AB = d$ and the area of the trapezium $PQRB$ is $\alpha$,then the ordered pair $(d, \alpha)$ 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:

$A$ tower subtends an angle $\alpha$ at a point $A$ in the plane of its base,and the angle of depression of the foot of the tower from a point $P$ at a height $l$ meters vertically above $A$ is $\beta$. The height of the tower is