$A$ flag is standing vertically on a tower of height $1 \ m$. At a point at a distance $2 \ m$ from the foot of the tower,the flag and the tower subtend equal angles. The height of the flag is (in meters):

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 poles standing on a horizontal ground are of heights $5 \, m$ and $10 \, m$ respectively. The line joining their tops makes an angle of $15^o$ with the ground. Then the distance (in $m$) between the poles is:

$A$ person standing at a distance of $10 \ m$ from a pole observes that the angle subtended by the lower $\frac{1}{3}$rd part and the upper $\frac{2}{3}$rd part of the pole are the same. Find the height of the pole.

The upper part of a tree broken by the wind makes an angle of $30^\circ$ with the ground. The distance from the root to the point where the top of the tree touches the ground is $10 \, m$. What was the original height of the tree in meters?

$A$ 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