Question

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.

Answer 1

Height of the building, PQ = 30m. 

Height of the boy, OA = 1.5m. 

If the position of Boy at OA, 

angle of elevation, ∠POR = 30°, 

His second position, OO’, ∠POR = 60°. 

RQ = OA = 1.5 m. 

∴ PR = 30 – RQ = 30 – 1.5 

PR = 28.5 m.

Distance he walked towards the building: OO’ = OR – O’R

Distance he walked towards the building: OO’ = 19√3m