$A$ $10 \ m$ long ladder is placed against a wall. It is inclined at an angle of $30^{\circ}$ to the ground. The distance (in $m$) of the foot of the ladder from the wall is (Given $\sqrt{3} = 1.732$)

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 tower of height $108 \; m$,the angles of depression of two objects on either side of the tower are $30^{\circ}$ and $45^{\circ}$. The distance between the objects is:

The length of a shadow of a vertical tower is $\frac{1}{\sqrt{3}}$ times its height. The angle of elevation of the Sun is (in $^{\circ}$)

Two posts are $x \text{ m}$ apart and the height of one is double that of the other. If from the midpoint of the line joining their feet,an observer finds the angular elevations of their tops to be complementary,then the height (in $\text{m}$) of the shorter post is

The distance between two pillars is $120 \text{ m}$. The height of one pillar is thrice the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in $\text{m}$) of the taller pillar is (Use: $\sqrt{3} = 1.732$)