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

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:

$A$ bird is sitting on the top of a vertical pole $20 \ m$ high and its angle of elevation from a point $O$ on the ground is $45^o$. It flies off horizontally straight away from the point $O$. After one second,the angle of elevation of the bird from $O$ is reduced to $30^o$. Then the speed (in $m/s$) of the bird is

The angle of elevation of the top of a tower from a point $A$ due north of it is $\alpha$ and from a point $B$ at a distance of $9$ units due west of $A$ is $\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)$. If the distance of the point $B$ from the tower is $15$ units,then $\cot \alpha$ is equal to.

If a flagstaff of $6 \ m$ high placed on the top of a tower throws a shadow of $2\sqrt{3} \ m$ along the ground,then the angle (in degrees) that the sun makes with the ground is.......$^o$

$A$ tree is broken by wind,its upper part touches the ground at a point $10 \ m$ from the foot of the tree and makes an angle of $45^\circ$ with the ground. The total length of the tree is: