Question

A boy of height 150cm is 8meter away from a lamp post. If the shadow castes is 2meter. Find the height of the lamp post

Answer 1

see attached figure,

AB is the height of lamp post.

EC is height of boy e.g., EC = 1.5m [ 150cm = 1.5m]

distance between boy and lamp post is 8m e.g., CB = 8m

and length of shadow caste is 2m e.g., CD = 2m

from ∆DCE and ∆DBA

$\angle{ABD}=\angle{ECD}$ = 90°

$\angle{ADB}=\angle{EDC}$

so, ∆BDA $\sim$ ∆CDE

so, AB/CE = BD/CD

or, h/1.5m = (8m + 2m)/2m

or, h/1.5m = 10m/2m

or, h = 7.5m

hence, height of lamp post = 7.5m

Answer 2

Answer:

7.5 m tall

Step-by-step explanation:

150 cm = 1.5 m

Define x:

Let x be the height of the lamp post

Find the angle θ:

tan θ = opp/adj

tan θ = 1.5/2

Find the height of the lamp post:

tan θ = opp/adj

1.5/2 = x/(2 + 8)

1.5/2 = x/10

x = 10 (1.5/2)

x = 7.5 m

Answer: The lamp post is 7.5 m tall