Ethan stands 256 cm at point C from a lamp post AB. He is 180 cm tall and his shadow from the lamp is 144 cm long. Find the height AB, in metres, of the lamp post.

Question

asked Nov 4, 2021 22.7k views

1 Answer

Saurabh Bayani · Answer 1 · 2021-11-09T06:59:12+0000

Answer:500 cm

Explanation:

Given

height of ethan = 180 cm

length of shadow =144 cm

Distance of ethan from lamp =256 cm

from diagram, we can write

$\Rightarrow tan \theta =(FC)/(EC)\quad \ldots(i)$

$\Rightarrow \tan \theta =(AB)/(BE)\quad \ldots (ii)$

From (i) and (ii) we get

$\tan \theta =(FC)/(EC)=(AB)/(BE)$

$\Rightarrow (180)/(144)=(h)/(144+256)$

$\Rightarrow h=(180)/(144)* 400$

$\Rightarrow h=500\ cm$

So, height of lamp post AB is
$500\ cm$