sir this is the important question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
The angle of elevation of a pillar from a point A on the ground is 45
and from a point B diametrically opposite to A
and on the other side of the pillar is 60.
Find the height of the pillar,
given that the distance between A and B is 15 m.
question no 27 , heights and distances , ICSE board
Consider CD as the pillar of x m
Angles of elevation of points A and B are 450 and 600
It is given that
AB = 15 m
Take AD = y
DB = 15 – y
In right triangle CAD
tan θ = CD/AD
Substituting the values
tan 450 = x/y
So we get
1 = x/y
x = y …… (1)
In triangle CDB
tan 600 = x/(15 – y)
Substituting the values
√3 = x/(15 – y)
So we get
x = √3 (15 – y) ….. (2)
Using both the equations
x = √3 (15 – x)
x = 15√3 – √3x
So we get
x + √3x = 15√3
x (1 + √3) = 15√3
x = 15√3/ (1 + √3)
We can write it as
x = (15 × 1.732)/ (1 + 1.732)
x = 25.98/2.732
x = 9.51
Hence, the height of the pillar is 9.51 m.