$A$ 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 $m$):

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

From the top of a $25 \ m$ high cliff,the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower in $m$.

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?

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 $m$)

The angle of elevation of the top of an unfinished tower at a point distant $120 \ m$ from its base is $45^{\circ}$. If the elevation of the top at the same point is to be $60^{\circ}$,the tower must be raised to a height of: