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

From the top of a $60 \ m$ high lighthouse with its base at sea level,the angle of depression of a boat is $15^{\circ}$. The distance of the boat from the lighthouse 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:

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.

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?