Question

If a 1.5-m-tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is ______.

Options

• 1.5 m

• 2 m

• 2.5 m

•  2.8 m

Answer 1

If a 1.5-m-tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is 2.5 m.

Explanation:

Let AB be the lamp post and CD = 1.5 m be the girl.

The given information can be represented as 

Here, shadow of girl is DE = 4.5 m and BD = 3 m. 

In `ΔCDE, tan θ=(CD)/(DE)=(1.5)/(4.5)`         .................(1) 

In `ΔABE, tan θ= (AB)/(BE)=(AB)/(4.5+3)=(AB)/7.5` ..........(2) 

From (1) and (2),

`1.5/4.5=(Ab)/7.5`

`⇒ AB=(1.5xx7.5)/4.5=2.5 m`