Observing from the top of a tower,the angle of depression of an object $30 \ m$ away from the base of the tower is found to be $45^\circ$. Find the height of the tower (in $m$).

$A$ $15\ m$ high eucalyptus tree standing erect on the ground breaks at the height of $5\ m$ from the ground. The broken part bends such that the top of the tree touches the ground. Find the angle made by the broken part of the tree with the ground. (in $^{\circ}$)

Write 'True' or 'False' and justify your answer.
If the length of the shadow of a tower is increasing,then the angle of elevation of the sun is also increasing.

The angles of depression of two boats $A$ and $B$ from the top of a lighthouse are $25^{\circ}$ and $40^{\circ}$ respectively. Then $\ldots \ldots \ldots \ldots$ from the lighthouse.

The union of the horizontal ray and the ray of vision forms the angle of elevation; then the object under observation is $\ldots \ldots \ldots . .$

During a storm,a $21 \,m$ high tree breaks but the broken part remains attached to the trunk and makes an angle of $30^{\circ}$ with the ground. At what height from the ground is the tree broken? (in $m$)