A man standing in one corner of a square football field observes that the angle subtended by a pole in the corner just diagonally opposite to this corner is 60°. When he retires 80 m from the corner, along the same straight line, he finds the angle to be 30°. The length of the field, in m, is :

The diagonal 'd' of the football field will be the adjacent side. The height of pole,h, will be the opposite side.
According to the given conditions,
h = d tan 60 and
h = (d+80) tan 30
Equationg, we get,
d tan 60 = d tan 30 + 80 tan 30
d (tan 60 - tan 30) = 80 tan 30
On substituting the values of tan 30 and tan 60, we get,
2d = 80
d = 40 m.
We know that side*$$\sqrt{2}$$ = 40
=> Side = $$20\sqrt{2}$$.
Option B is the right answer.