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A person is standing in a room of width 200 cm. A plane mirror of vertical length 10 cm is fixed on a wall in front of the person. The person looks into the mirror from distance 50 cm. How much width (height) of the wall behind him will he be able to see : (assume that he uses the full mirror) (A) 30 cm (B) 40 cm (C) 50 cm (D) None

 A person is standing in a room of width 200 cm. A plane mirror of vertical length 10 cm is fixed on a wall in front of the person. The person looks into the mirror from distance 50 cm. How much width (height) of the wall behind him will he be able to see : (assume that he uses the full mirror)
(A) 30 cm (B) 40 cm (C) 50 cm (D) None
 

Grade:12

1 Answers

Arun
25750 Points
4 years ago
Width of the room = 200cm (Given)
 
Length of plane mirror = 10cm  (Given)
 
Distance of the person looking into mirror = 50cm  (Given)
 
In first triangle -
 
TanФ = x/200 --- 1
 
In second triangle -
 
TanФ = 5/50 --- 2
 
Equating both the equations -
 
5/50 = x/200
 
x = 20cm
 
Thus, the height of the wall is 2x+10 = 50
 
The width of the wall he will be able to see = 50cm

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