sir this is the important question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances

A man observes the angles of elevation of the top of a building to be 300.

He walks towards it in a horizontal line through its base.

On covering 60 m the angle of elevation changes to 600.

Find the height of the building correct to the nearest decimal place.

question no 20 , heights and distances , ICSE board

It is given that

AB is a building

CD = 60 m

In triangle ABC

tan 60

^{0}= AB/BC√3 = AB/BC

So we get

BC = AB/√3 ….. (1)

In triangle ABD

tan 30

^{0}= AB/BD1/√3 = AB/ (BC + 60)

By cross multiplication

BC + 60 = √3 AB

BC = √3 AB – 60

Using both the equations we get

AB/√3 = √3 AB – 60

By further calculation

AB = 3AB – 60√3

3AB – AB = 60 × 1.732

So we get

AB = (60 × 1.732)/ 2

AB = 51.96 m