Trignometry

let height of lamp post = h

and its distance from center of the road = x

here lamp focus covers a total area within 30^o so the horizontal distance which is covered by light of lamp should be 10m

so at 10m distance the angle made by lamp on the boundary point will be 90-30 = 60

so we have tan 45 = h/x

and tan 60 = h/10    => h= 10 tan60 = 103

so l=h=103