Question

if a 1.5 m tall girl stands at a distance of 3m from a lamp post and casts a shadow of length 4.5 m on the ground then find the height of the lamp-post please also give the explanation with the solution​

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 = 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

Answer you can help

Answer 2

Answer: 2.5 m

Step-by-step explanation:

Let AB be the girl and CD be the lamp.

OD = OB + OD = 7.5 m

BD = 3 m

OB = 4.5 m

In Triangle OAB,

Tan ∅ = AB/OB = 1.5/4.5 = 1/3

In Triangle OCD,

Tan ∅ = CD/OD = CD/7.5

CD/OD = AB/OB

CD/7.5 = 1/3

CD = 7.5/3

CD = 2.5m

Therefore,

The height of the lamp post is 2.5m

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