$A$ 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 $^\circ$)

The angle of elevation of the top of a vertical pole as observed from a point $20\, m$ away from the base of the pole is $60^\circ$. Find the height of the pole. (in $m$)

$A$ boat is sailing with constant speed towards a man sitting on a tree on the river bank. At some moment,the man measures the angle of depression of the boat as $30^{\circ}$. $10$ minutes later,this angle is measured as $60^{\circ}$. How much longer will the boat now take to reach the bank? (in $min$)

The angle of elevation of the top of a pole from a point $x \, m$ away from the base of the pole is $60^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

$A$ statue,$1.6 \, m$ tall,stands on the top of a pedestal. From a point on the ground,the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$. Find the height of the pedestal.

From a point on the ground,the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20 \, m$ high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.