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Question
A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamppost. The girl whose height is 1.25 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamppost are in the same line, find the height of the lamp post.
Solution
Let the height of the tower ED be “x” m.
In ∆ABC and ∆EDC.
∠ABC = ∠CED = 90° ...(vertical Pole)
∠ACB = ∠ECD ...(Laws of reflection)
∆ABC ~ ∆DEC
`"AB"/"DE" = "BC"/"EC"`
`1.5/x = 0.4/87.6`
x = `(1.5 xx 87.6)/(0.4)`
= `(1.5 xx 876)/4`
= 1.5 × 219
= 328.5
The height of the Lamp Post = 328.5 m
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