$A$ person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is $60^{\circ}$. When he moves $40 \ m$ away from the bank,he finds the angle of elevation to be $30^{\circ}$. The breadth of the river is (in $m$):

$A$ person walking along a straight road towards a hill observes at two points,separated by a distance of $\sqrt{3} \text{ km}$,that the angles of elevation of the hill are $30^{\circ}$ and $60^{\circ}$. The height of the hill is

The angle of elevation of a tower from a distance $50 \; m$ from its foot is $30^{\circ}$. The height of the tower is

The distance between two pillars is $120 \text{ m}$. The height of one pillar is thrice the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in $\text{m}$) of the taller pillar is (Use: $\sqrt{3} = 1.732$)

$A$ man having height $169 \; cm$ is standing near a pole. He casts a shadow $130 \; cm$ long. What is the length (in $cm$) of the pole if it casts a shadow $420 \; cm$ long?

The angles of depression from the top of a lighthouse to two boats,which are $60 \, m$ apart and in the same direction (due east),are $45^{\circ}$ and $30^{\circ}$. The height of the lighthouse is: