A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

Let PQ is building and AS is a boy 1.5 m tall. He moves from S to towards building.
Here, PQ = 30m
Therefore, PR = PQ – RQ = (30 – 1.5) m = 28.5 m = 57/2 m
In ΔPAR,
PR/AR = tan 30° ⇒ (57/2)/AR = 1/√3 ⇒ AR = 57√3/2
In ΔPRB,
PR/BR = tan 60° ⇒ (57/2)/BR = √3 ⇒ BR = 57/2√3 = 57√3/6 = 19√3/2
Distance walked towards the building
= ST = AB = AR – BR = 58√3/2 – 19√3/2 = 38√3/2 = 19√3
Hence, the distance walked towards the building is 19√3 m.