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

From the base of a pole of height $20 \text{ m}$,the angle of elevation of the top of a tower is $60^{\circ}$. The pole subtends an angle of $30^{\circ}$ at the top of the tower. Then the height of the tower is

The angle of elevation of a stationary cloud from a point $2500 \, m$ above a lake is $15^\circ$ and the angle of depression of its reflection in the lake is $45^\circ$. The height of the cloud above the lake level is

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 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 angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is