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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
Solution
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`
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