At a distance $2h$ from the foot of a tower of height $h$,the tower and a pole at the top of the tower subtend equal angles. The height of the pole is:

From the top of a lighthouse $60 \ m$ high with its base at the sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

$A$ tower $50 \ m$ high stands on the top of a mount. From a point on the ground,the angles of elevation of the top and bottom of the tower are found to be $75^o$ and $60^o$ respectively. The height of the mount is:

The length of the shadow of a pole inclined at $10^\circ$ to the vertical towards the sun is $2.05 \text{ m}$,when the elevation of the sun is $38^\circ$. The length of the pole is

$A$ tower $PQ$ stands on a horizontal ground with base $Q$ on the ground. The point $R$ divides the tower into two parts such that $QR = 15 \, m$. If from a point $A$ on the ground,the angle of elevation of $R$ is $60^{\circ}$ and the part $PR$ of the tower subtends an angle of $15^{\circ}$ at $A$,then the height of the tower is:

$ABCD$ is a rectangular field. $A$ vertical lamp post of height $12\,m$ stands at the corner $A$. If the angle of elevation of its top from $B$ is $60^\circ$ and from $C$ is $45^\circ$,then the area of the field is