sir this is the important question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
this is important question since is has been asked in previous year exam
A man 1.8 m high stands at a distance of 3.6 m from a lamp post
and casts a shadow of 5.4 m on the ground.
Find the height of the lamp post.
question no 31 , heights and distances , ICSE board
Consider
AB as the lamp post
CD is the height of man
BD is the distance of man from the foot of the lamp
FD is the shadow of man
Construct CE parallel to DB
Take AB = x and CD = 1.8 m
EB = CD = 1.8 m
AE = x – 1.8
Shadow FD = 5.4 m
In right triangle ACE
tan θ = AE/CE
Substituting the values
tan θ = (x – 1.8)/ 3.6 …… (1)
In right triangle CFD
tan θ = CD/FD
Substituting the values
tan θ = 1.8/5.4 = 1/3 ….. (2)
Using both the equations
(x – 1.8)/ 3.6 = 1/3
So we get
3x – 5.4 = 3.6
3x = 3.6 + 5.4 = 9.0
By division
x = 9/3 = 3.0
Hence, the height of lamp post is 3 m.
I hope this helps!!!!