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

Answer:

let AB=CD= EQ = 1.5 m

Let dist. covered by boy is BD=x

Let BD=AC=x

Let DQ=CE=y

In fig. PE=30-1.5=28.5m

Angles are 30° and 60°

In ∆ PAE

tan 30 = PE/AE

1/√3=28.5/x+y

28.5√3=x+y –(1)

In ∆PCE

tan60=PE/CE

√3=28.5/y

y=28.5/√3

Put in (1)

x+28.5/√3=28.5√4

x=(28.5×3-28.5)/√3

= (85.5-28.5)/√3

=57/√3

Rationalize

=57/√3×√3/√3

=57√3/3

=19√3

hope this helps you