Solution:

Let the boy to stand initially at point Y with a 30° inclination before approaching the building at point X with a 60° inclination.

To Find: XY i.e. the distance walked by the boy towards the building.

From figure,

CD = XY.

Building’s height = AZ = 30 m.

AZ – BZ = AB

= 30 – 1.5 = 28.5

AB = 28.5 m

In right angle ΔABD,

AB/BD = tan 30°

28.5/BD = 1/√3

BD = 28.5√3 m

Again,

In right angle ΔABC,

AB/BC = tan 60°

28.5/BC = √3

BC = 28.5/√3 = 28.5√3/3

As a result, BC’s length is 28.5√3/3 m.

XY = CD = BD – BC = (28.5√3-28.5√3/3) = 28.5√3(1-1/3) = 28.5√3 × 2/3 = 57/√3 = 19√3  m.

As a result, 19√3 is m the distance walked by the boy towards the building.