$A$ $10 \ m$ 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 height of a tower is $100 \text{ m}$. When the angle of elevation of the sun changes from $30^{\circ}$ to $45^{\circ}$,the shadow of the tower becomes $x \text{ m}$ smaller. The value of $x$ is (in $\text{m}$):

$A$ tower is $30 \ m$ high. An observer from the top of the tower makes an angle of depression of $60^{\circ}$ at the base of the building and an angle of depression of $45^{\circ}$ at the top of the building. What is the height of the building in metres?

The angle of elevation of the top of a $TV$ tower from three points $A, B, C$ in a straight line through the foot of the tower are $\alpha, 2 \alpha, 3 \alpha$ respectively. If $AB = a$,the height of the tower is

From a point $P$ on the ground,the angle of elevation of the top of a $10 \ m$ tall building is $30^{\circ}$. $A$ flag is hoisted at the top of the building,and the angle of elevation of the top of the flagstaff from $P$ is $45^{\circ}$. Find the length of the flagstaff. (Take $\sqrt{3} = 1.732$) (In $m$)

The ratio of the length of a rod and its shadow is $1 : \sqrt{3}$. The angle of elevation of the sun is (in $^{\circ}$)