Question

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.

Answer 1

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`