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 $m$.

When the length of the shadow of a pole is equal to the height of the pole,then the angle of elevation of the source of light is: (in $^{\circ}$)

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

From the top of a $60 \ m$ high lighthouse with its base at sea level,the angle of depression of a boat is $15^{\circ}$. The distance of the boat from the lighthouse is

$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^{\circ}$. After some time,the angle of depression becomes $60^{\circ}$. The distance (in $m$) travelled by the car during this time is

The angle of elevation of the top of a tower at a point $G$ on the ground is $30^{\circ}$. On walking $20 \ m$ towards the tower,the angle of elevation becomes $60^{\circ}$. The height of the tower is equal to