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Solution: In your question, time is not given. So let's find the length of shadow after t second.

Let the boy of height 90cm be at point D on the ground from the lamp post after t sec.

Let time t=4 sec.
∴ AD = 1.2 m/sec × 4 sec = 4.8 m = 480 cm
 
Suppose the length of the shadow of the boy be x cm when he at position D.
 
∴ BD = x cm
 
In ∆BDE and ∆BAC
 
∠BDE = ∠BAC (90°)
 
∠DBE = ∠ABC (Common)
 
∴ ∆BDE ∼ ∆BAC (AA similarity)
 
BE / BC = DE / AC = BD / AB  ( Corresponding sides are proportional )
 
90 / 360 = x / (480 + x)
 
1 /  4 = x / (480 + x)
 
4x = 480 + x
 
x = 480 / 3 = 160
 
∴ Length of boy shadow after 4 second is 160 cm.

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