Let AB and ED be two pillars each of height h metres Let C be a point on he road BD such that
BC=x metres Then CD=(100−x) metres Given ∠ACB=60∘ and ∠ECD=30∘
In ΔABC,tan60∘=ABBC ⇒√3=hx⇒h=√3x..........(i)
In ΔECD,tan30∘=EDCD ⇒1√3=h100−x⇒h√3=100−x...........(ii)
∴ Subst. the value of h from (i) in (ii) we get
√3x×√3=100−x⇒3x=100−x⇒4x=100⇒x=25m
∴ h=(√3×25)=25×1.732m=43.3m
∴ The required point is at a distance of 25 m from the pillar B and the height of each pillar is 43.3m