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 $m$.

At a point,$15 \, m$ away from the base of a $15 \, m$ high house,the angle of elevation of the top is (in $^{\circ}$)

From an aeroplane vertically over a straight horizontal road,the angles of depression of two consecutive milestones on the opposite sides of the aeroplane are observed to be $30^{\circ}$ and $60^{\circ}$. Find the height in miles of the aeroplane above the road.

$A$ person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is $60^{\circ}$. When he moves $40 \ m$ away from the bank,he finds the angle of elevation to be $30^{\circ}$. The breadth of the river is (in $m$):

The shadow of a tower standing on a level ground is found to be $40 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ}$. Find the length of the tower. (In $m$)

$A$ man standing at a point $P$ (or $L$ in the diagram) is watching the top of a tower $N$,which makes an angle of elevation of $30^{\circ}$ with the man's eye. The man walks some distance towards the tower to point $Q$ to watch its top and the angle of elevation becomes $60^{\circ}$. What is the distance (in units) between the base of the tower $M$ and the point $P$ (or $L$)?