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 $m$):

$A$ 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 tops of two poles of height $60 \ m$ and $35 \ m$ are connected by a rope. If the rope makes an angle with the horizontal whose tangent is $\frac{5}{9}$,then what is the distance (in $m$) between the two poles?

If $r \sin \theta = 1$ and $r \cos \theta = \sqrt{3}$,then the value of $(\sqrt{3} \tan \theta + 1)$ is

Two posts are $x \text{ m}$ apart and the height of one is double that of the other. If from the midpoint of the line joining their feet,an observer finds the angular elevations of their tops to be complementary,then the height (in $\text{m}$) of the shorter post is

The angle of elevation of the sun when the length of the shadow of a pole is equal to its height is