The angle of elevation of the sun,when the shadow of the pole is $\sqrt{3}$ times the height of the pole,is ....$^o$

$A$ tower subtends angles $\alpha, 2\alpha, 3\alpha$ respectively at points $A, B$ and $C$,all lying on a horizontal line through the foot of the tower. Then $AB/BC = $

$A$ $20 \ m$ long tree is broken by the wind such that its top touches the ground at an angle of $30^\circ$. The height from the ground at which the tree is broken is:

$A$ flag-staff $5 \ m$ high stands on a building of height $25 \ m$. An observer at a height of $30 \ m$ observes that the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff 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 ..... $m$.

The tops of two poles of height $20 \ m$ and $14 \ m$ are connected by a wire. If the wire makes an angle $30^{\circ}$ with the horizontal,then the length of the wire is $... \ m$.