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 600 = AB/BC
√3 = AB/BC
So we get
BC = AB/√3 ….. (1)
In triangle ABD
tan 300 = AB/BD
1/√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