Question

A 1.5 m tall boy stands at a distance of 2 m from lamp post and casts a shadow of 4.5 m on the ground. Find the height of the post?

Answer 1

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 = 2 m

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 + 2)

=> CD = 7.5/2 = 3.75 m