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.

Question

Philoid · Accepted Answer

_{Let the initial point of boy is Z and final point is x}

_{Z x is the distance he walked.}

_{OP = OY-PY}

_{OP = 30-1.5} _⇒ _{28.5 m.}

_{In ∆OPA,}

tan 30° =

=

AP = ------------(1)

_{In ∆OPB,}

tan 60° =

√3 =

PB =

PB = m.

AB = AP-BP

AB = 28.5√3 -

AB = 28.5 ⇒ 28.5√3×

AB = ⇒ 19√3 m.

Therefore the walking distance of boy is 19√3 m.