$A$ man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^{\circ}$. When he moves $36 \ m$ away from the bank,he finds the angle to be $30^{\circ}$. Find the breadth of the river (in $m$).

The length of a shadow of a vertical tower is $\frac{1}{\sqrt{3}}$ times its height. The angle of elevation of the Sun is (in $^{\circ}$)

The angles of elevation of the top of a tower from the points $P$ and $Q,$ at distances of $a$ and $b$ respectively from the base of the tower and in the same straight line with it,are complementary. The height of the tower is

From the top of a tower of height $108 \; m$,the angles of depression of two objects on either side of the tower are $30^{\circ}$ and $45^{\circ}$. The distance between the objects is:

$A$ tower stands on a horizontal plane. $A$ man on the ground $100 \ m$ from the base of the tower finds the angle of elevation of the top of the tower to be $30^{\circ}$. What is the height of the tower (in $m$)?

An observer on the top of a cliff,$200 \, m$ above the sea level,observes the angle of depression of two ships at anchor to be $45^{\circ}$ and $30^{\circ}$ respectively. Find the distance (in $m$) between the ships if the line joining them stretches to the base of the cliff.