Question

A 150cm tall boy stands at a distance of 8 m from a lamp post and cast a shadow of 2m, find the height of lamp post

Answer 1

Height of the boy = 1.5m

Distance of the boy and lamp post = 8m.

Length of shadow = 2m.

tanθ = 1.5/2 = 0.75 {height of the boy is perpendicular and shadow is base}

Also tanθ = (Height of the lamp post)/(8+2) = (Height of the lamp post)/10

or, (Height of the lamp post)/10 = 0.75

or, Height of the lamp post = 7.5m [Ans]

∵ The height of the lamp post is 7.5m.

Answer 2

Thank you for asking this question.

Here is your answer:

Let AB be boy = 1.5m

CD be lamp = Let it be x m.

OB be shadow cast by boy = 4.5m

BD be distance between boy and lamp = 3m

Therefore

In ΔAOB,

= tan θ = AB/OB

In ΔCOD,

= tan θ = CD/OD = CD/(OB+BD)

∴ AB/OB = CD/(OB+BD)

=1.5/4.5 = CD/(4.5+3)

= CD = 7.5/3 = 2.5m

If there is any confusion please leave a comment below.