The angle of elevation of the top of a tower from a point $20 \ m$ away from its base is $45^\circ$. The height of the tower is ....... $m$.

$A$ person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^\circ$. When he moves $40 \ m$ away from the bank,he finds the angle to be $30^\circ$. The breadth of the river is.....$m$

The angle of elevation of the top of the tower observed from each of the three points $A, B, C$ on the ground,forming a triangle,is the same angle $\alpha$. If $R$ is the circum-radius of the $\Delta ABC$,then the height of the tower is

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object,the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

An eagle flying $100 \ m$ above the ground looks at its prey on the ground at an angle of depression of $30^\circ$. After flying a distance of $'x' \ m$ towards the prey at the same height,the angle of depression becomes $45^\circ$. The value of $x$ will be:

The angles of elevation of the top of a tower from three collinear points $A, B$,and $C$ on a road leading to the foot of the tower are $30^{\circ}, 45^{\circ}$,and $60^{\circ}$ respectively. The ratio of $AB$ to $BC$ is