The angle of elevation of a tower from a point $A$ due south of it is $30^\circ$ and from a point $B$ due west of it is $45^\circ$. If the height of the tower is $100 \ m$,then $AB = \dots \ m$.

An aeroplane flying at a constant speed,parallel to the horizontal ground,$\sqrt{3} \ km$ above it,is observed at an elevation of $60^\circ$ from a point on the ground. If,after five seconds,its elevation from the same point is $30^\circ$,then the speed (in $km/hr$) of the aeroplane is

The angle of elevation of a point situated at a distance of $70 \ m$ from the base of a tower is $45^\circ$. The height of the tower is ..... $m$.

From the top of a hill $h$ metres high,the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$,all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to:

The horizontal distance between two towers is $60 \ m$. The angle of depression of the top of the first tower as seen from the top of the second tower is $30^\circ$. If the height of the second tower is $150 \ m$,then the height of the first tower is: