From the top of a lighthouse $30 \ m$ high with its base at sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

$A$ 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......$m$.

$A$ man is walking towards a vertical pillar in a straight path,at a uniform speed. At a certain point $A$ on the path,he observes that the angle of elevation of the top of the pillar is $30^o$. After walking for $10 \text{ minutes}$ from $A$ in the same direction,at a point $B$,he observes that the angle of elevation of the top of the pillar is $60^o$. Then the time taken (in minutes) by him,from $B$ to reach the pillar,is:

$A$ flag-staff $5 \ m$ high stands on a building of height $25 \ m$. An observer at a height of $30 \ m$ observes that the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff is:

$A$ ladder rests against a wall making an angle $\alpha$ with the horizontal. The foot of the ladder is pulled away from the wall through a distance $x$,so that it slides a distance $y$ down the wall making an angle $\beta$ with the horizontal. The correct relation is

Two vertical poles $AB = 15 \ m$ and $CD = 10 \ m$ are standing apart on a horizontal ground with points $A$ and $C$ on the ground. If $P$ is the point of intersection of $BC$ and $AD$,then the height of $P$ (in $m$) above the line $AC$ is: