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..........

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 $, m$)

$A$ $1.2\, m$ tall girl spots a balloon moving with the wind in a horizontal line at a height of $88.2\, m$ from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$. After some time,the angle of elevation reduces to $30^{\circ}$ (see $Fig.$). Find the distance travelled by the balloon during the interval.

$A$ cable tied to the top of an electric pole is fixed at a point on the ground. The length of the cable is $22\, m$ and it makes an angle of measure $30^{\circ}$ with the ground. Find the height of the electric pole (in $m$).

From a point $A$ on the ground,the angle of elevation of the top of a tower is found to be $45^{\circ}$. If the distance between point $A$ and the base of the tower is $x$ and the height of the tower is $y$,then which of the following holds true?

$A$ $TV$ tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower,the angle of elevation of the top of the tower is $60^{\circ}$. From another point $20 \, m$ away from this point on the line joining this point to the foot of the tower,the angle of elevation of the top of the tower is $30^{\circ}$ (see figure). Find the height of the tower and the width of the canal.