$A$ pole stands vertically on the ground. The length of the shadow of the pole is $\frac{1}{\sqrt{3}}$ times the height of the pole. Then,the angle of elevation of the sun is $\ldots \ldots \ldots \ldots . . .$ (in $^\circ$)

$A$ pole stands erect on the ground. $A$ wire tied to the top of the pole is affixed at a point on the ground. If the length of the wire is $7 \, m$ and the wire makes an angle of $30^{\circ}$ with the ground,find the height of the pole (in $m$).

Two poles are $x$ metres apart and the height of one is double than that of the other. If from the midpoint of the line joining their feet,an observer finds the angle of elevation of their tops to be complementary,then the height of the shorter pole is $\ldots \ldots \ldots \ldots$

Watching from the top of the $x \ m$ high building,the angle of depression of a child on the ground is found to be $\theta$. Then,the distance of the child from the base of the building is..........

$A$ pole stands slanting on the ground making an angle of $60^{\circ}$ with the ground. At high noon,the length of the shadow of the pole is $3 \, m$. Find the length of the pole in $m$.

The approximate value of $\sqrt{3}$ up to $2$ decimal places is $\ldots \ldots \ldots$