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 $^{\circ}$)

The angle of elevation of a ladder leaning against a house is $60^{\circ}$ and the foot of the ladder is $6.5 \ m$ from the house. Find the length of the ladder in metres.

The angle of elevation of an aeroplane as observed from a point $30 \ m$ above the transparent water surface of a lake is $30^{\circ}$ and the angle of depression of the image of the aeroplane in the water of the lake is $60^{\circ}$. The height of the aeroplane from the water surface of the lake is (in $m$):

$A$ person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is $60^{\circ}$. When he moves $40 \ m$ away from the bank,he finds the angle of elevation to be $30^{\circ}$. The breadth of the river is (in $m$):

$A$ man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of $45^{\circ}$ with the man's eye when at a distance of $60 \ m$ from the tower. After $5 \ s$,the angle of depression becomes $30^{\circ}$. What is the approximate speed (in $km/hr$) of the boat,assuming that it is running in still water?

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 $^{\circ}$)