$A$ pole stands vertically inside a triangular park $ABC$. If the angle of elevation of the top of the pole from each corner of the park is the same,then in the $\Delta ABC$,the foot of the pole is at the

$A$ vertical pole of height $h$ stands on a building of height $H$. The angle of elevation of the top of the building from a point on the ground,which is $5$ units away from the foot of the building,is $\alpha$. The pole subtends an angle $\beta$ at the same point on the ground. If $2 \tan \beta \cot \alpha = 1$,then-

$A$ tower, of $x$ metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then, the length of the flagstaff (in metres) is:

The horizontal distance between two towers is $60 \ m$. The angle of depression of the top of the first tower as seen from the top of the second tower is $30^\circ$. If the height of the second tower is $150 \ m$,then the height of the first tower 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

If the angle of depression of a point $A$ on the ground from the top of a tower is $30^\circ$,then the angle of elevation of the top of the tower from the point $A$ will be .............. $^\circ $.