$A$ 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:

$A$ horizontal park is in the shape of a triangle $OAB$ with $AB = 16$. $A$ vertical lamp post $OP$ is erected at the point $O$ such that $\angle PAO = \angle PBO = 15^{\circ}$ and $\angle PCO = 45^{\circ}$,where $C$ is the midpoint of $AB$. Then $(OP)^{2}$ is equal to.

$A$ house subtends a right angle at the window of an opposite house. The angle of elevation of the window from the bottom of the first house is $30^{\circ}$. If the distance between the two houses is $6 \ m$,then the height of the first house is:

The tops of two poles of height $20 \ m$ and $14 \ m$ are connected by a wire. If the wire makes an angle $30^{\circ}$ with the horizontal,then the length of the wire 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:

$A$ person observes the angle of elevation of a building as $30^\circ$. The person proceeds towards the building with a speed of $25(\sqrt{3} - 1) \, m/hour$. After $2 \, hours$,he observes the angle of elevation as $45^\circ$. The height of the building (in meters) is: