$A$ ladder leans against a wall such that its lower end makes an angle of measure $\theta$ with the ground. If its lower end is $a \ m$ away from the base of the wall,then the ladder reaches the wall at a height of $\ldots \ldots \ldots \ldots \ldots \ m$.

Watching from the top of the $x \ m$ high building,the angle of depression of a child on the ground is found to be $\theta$. Then,the distance of the child from the base of the building is..........

In $\Delta ABC$,$\angle B$ is a right angle. If $AC = 16$ and $BC = 8$,then $m \angle C = \dots$ (in $^{\circ}$)

Two ships are anchored in the opposite directions from a lighthouse. The angle of depression of one ship from the top of the lighthouse is $60^{\circ}$ and that of the other ship from the same place is found to be $30^{\circ}$. If the ship with the angle of depression of $60^{\circ}$ is $150\,m$ away from the lighthouse,find the distance between these two ships (in $m$).

$A$ person is watching from a point $A$ on the ground,which is $x \ m$ away from the base of a building. The height of the building is $y \ m$ and the angle of elevation of the top of the building is found to be $70^\circ$. Then:

$A$ $4 \, m$ long ladder leans on a wall such that its lower end remains $2 \, m$ away from the base of the wall. Then,the ladder makes an angle of measure $\ldots \ldots$ with the ground. (in $^\circ$)