The angle of elevation of the top of the temple on the bank of the river from a point exactly opposite to the temple on the other bank of the river is $30^{\circ}$. If the height of the temple is $20 \ m$,then the breadth of the river is $\ldots \ldots \ldots \ldots \ m$.

$A$ window of a house is $h$ meters above the ground. From the window,the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be $\alpha$ and $\beta$,respectively. Prove that the height of the other house is $h(1 + \tan \alpha \cot \beta)$ meters.

Write 'True' or 'False' and justify your answer.
The angle of elevation of the top of a tower is $30^{\circ}$. If the height of the tower is doubled,then the angle of elevation of its top will also be doubled.

An erect tree is $300\, m$ away from a hill. If the height of the hill is $300\, m$,find the angle of depression of the base of the tree from the top of the hill. (in $^{\circ}$)

When the angle of elevation of the sun is $30^{\circ}$,the length of the shadow of a tower is $90\, m$. Find the height of the tower. (in $m$)

The height of a tower is $60 \, m$. From a point on the ground,the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the distance of that point from the base of the tower. (in $m$)