Answer :
Answer:500 cm
Step-by-step explanation:
Given
height of ethan = 180 cm
length of shadow =144 cm
Distance of ethan from lamp =256 cm
from diagram, we can write
[tex]\Rightarrow tan \theta =\frac{FC}{EC}\quad \ldots(i)[/tex]
[tex]\Rightarrow \tan \theta =\frac{AB}{BE}\quad \ldots (ii)[/tex]
From (i) and (ii) we get
[tex]\tan \theta =\frac{FC}{EC}=\frac{AB}{BE}[/tex]
[tex]\Rightarrow \frac{180}{144}=\frac{h}{144+256}[/tex]
[tex]\Rightarrow h=\frac{180}{144}\times 400[/tex]
[tex]\Rightarrow h=500\ cm[/tex]
So, height of lamp post AB is [tex]500\ cm[/tex]
