$A$ ladder leans on a wall to reach a height of $3 \, m$ on the wall. If the ladder makes an angle of $30^{\circ}$ with the ground,the length of the ladder is ........... $m$.

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 $\ldots \ldots \ldots \ldots \ m$.

'True' or 'False' and justify your answer.
If a man standing on a platform $3 \ m$ above the surface of a lake observes a cloud and its reflection in the lake,then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Observing from the top of a $150\, m$ high tower,the angle of depression of a cycle on the ground is found to be $60^{\circ}$. How far away is the cycle from the tower?

The angle of depression of a car parked on the road as observed from the top of a building is $60^{\circ}$. The angle of depression of that car from a window $14.6 \, m$ below the top is $45^{\circ}$. Find the distance between the car and the building (in $m$).

The shadow of a tower standing on a level ground is found to be $40 \, m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $60^{\circ} .$ Find the height of the tower.