$A$ house of height $100 \ m$ subtends a right angle at the window of an opposite house. If the height of the window is $64 \ m$,then the distance between the two houses is......$m$.

From an aeroplane vertically over a straight horizontal road,the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be $\alpha$ and $\beta$. Then,the height in miles of the aeroplane above the road 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 $PQ$ 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:

If the angle of elevation of a cloud from a point $P$ which is $25 \, m$ above a lake is $30^o$ and the angle of depression of the reflection of the cloud in the lake from $P$ is $60^o$,then the height of the cloud (in meters) from the surface of the lake is:

The angle of elevation of the top of a mobile tower from three points $P, Q$ and $R$ (on a straight line through the foot of the tower) are $\alpha, \beta$ and $\gamma$ respectively. If all three points lie on the same side of the foot of the tower and $\alpha : \beta : \gamma = 1 : 2 : 3$ and $PQ = l$,then the height of the tower is -