$A$ 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:

In a triangular park $PQR$,$PQ = PR = 200 \ m$. $A$ $TV$ tower stands at the mid-point $M$ of $QR$. If the angles of elevation of the top of the tower at $P, Q,$ and $R$ are $45^o, 30^o,$ and $30^o$ respectively,then the height of the tower (in $m$) is:

Two vertical poles of equal heights are $120 \, m$ apart. On the line joining their bottoms,$A$ and $B$ are two points. The angle of elevation of the top of one pole from $A$ is $45^\circ$ and that of the other pole from $B$ is also $45^\circ$. If $AB = 30 \, m$,then the height of each pole is.....$m$.

The angle of depression of a ship from the top of a tower $30 \, m$ high is $60^\circ$. Find the distance of the ship from the base of the tower.

$A$ ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of $60^{\circ}$ with the horizontal and the height of the house is $6\sqrt{3} \text{ m}$,then the length of the ladder is ..... $m$.

The sum of the angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then,the height of the tower is