In right-angled $\Delta ABC$,$m\angle B = 90^\circ$. If $AC = 20$ and $m\angle C = 30^\circ$,then $BC = \ldots$

Watching from the top of a building and from a window $10 \, m$ below the top,the angles of depression of a car on the ground are found to be $60^{\circ}$ and $45^{\circ}$ respectively. Find the distance of the car from the building. (in $m$)

There is a flag-post on the top of a $10 \, m$ high tower. From a point on the ground,the angle of elevation of the top of the tower is $45^{\circ}$ and that of the top of the flag-post is $60^{\circ}$. Find the height of the flag-post. (in $, m$)

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

As observed from a hill $340 \ m$ high,the angles of depression of two houses situated to the east and west of the hill are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the distance between the two houses. (in $m$)

As observed from the top of a building,the angle of depression of a man standing $10 \, m$ away from the building is found to be $45^{\circ}$. Find the height of the building (in $m$).