In a rectangle,if the angle between a diagonal and a side is $30^{\circ}$ and the length of the diagonal is $6 \text{ cm}$,the area (in $\text{cm}^2$) of the rectangle is:

$A$ tower stands at the end of a straight road. The angles of elevation of the top of the tower from two points on the road $500 \ m$ apart are $45^{\circ}$ and $60^{\circ},$ respectively. Find the height of the tower.

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 $m$):

From a point $P$ on the ground,the angle of elevation of the top of a $10 \ m$ tall building is $30^{\circ}$. $A$ flag is hoisted at the top of the building,and the angle of elevation of the top of the flagstaff from $P$ is $45^{\circ}$. Find the length of the flagstaff. (Take $\sqrt{3} = 1.732$) (In $m$)

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

$A$ man is standing near a $6 \, m$ long pole which casts an $8 \, m$ long shadow. If the man casts a shadow of $2.4 \, m$,what is the height of the man (in $m$)?