Two poles of height $7 \ m$ and $12 \ m$ stand on a plane ground. If the distance between their feet is $12 \ m$,the distance between their tops will be (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 $^{\circ}$)

$A$ 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?

From a point $P$ on a level ground,the angle of elevation of the top of a tower is $30^{\circ}$. If the tower is $100 \ m$ high,the distance (in $m$) of point $P$ from the foot of the tower is:

Two towers of equal height stand on either side of a wide road which is $100 \, m$ wide. At a point on the road between the towers, the angles of elevation of the tops of the towers are $60^{\circ}$ and $30^{\circ}$. Find their heights in metres. (in $\sqrt{3}$)

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