The length of a ladder is $6 \,m$ and it leans on a wall to reach the height of $3.6 \,m$. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

From a point on a bridge across a river,the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$,respectively. If the bridge is at a height of $3 \, m$ from the banks,find the width of the river.

When observed from the top of a tower,the angles of depression of two houses $A$ and $B$ in the Eastern and Western directions are $30^{\circ}$ and $60^{\circ}$ respectively. Then........

From a point $A$,$h \text{ m}$ above the ground level,the angle of elevation of the top of a tower is $\alpha$ and the angle of depression of the base of the tower is $\beta$. Prove that the height of the tower is $\frac{h(\tan \alpha + \tan \beta)}{\tan \beta} \text{ m}$.

$A$ $TV$ 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.

Observing an object from the point of observation,if one gets the angle of depression,then the object under observation is.........