Question

U.ONT
A plane mirror 50 cm long, is hung on a vertical wall of a room, win
ground. A man stands infront of the mirror at a distance 2 m awd
on a vertical wall of a room, with its lower edge 50 cm above the
niront of the mirror at a distance 2 m away from the mirror. If his eyes are at a
height 1.8 m above the ground, then the length (distance between
len the length (distance between the extreme points of the visible
om the mirror ism
region perpendicular to the mirror) of the floor visible to him due to reflection on
26
Find the value of x.​

Answer 1

Answer:

Explanation:

=> According to the diagram:

tan θ1 = 1.8 / 2+y

tan θ2 = 1.8 / 2+x+y

=> Take smaller triangles in consideration  :

tan θ1 = 0.5 / y = 1/2*y

tan θ2 = 1 / x + y

=> Therefore,

1.8 / 2+y = 1 / 2y  

3.6 y = 2 + 1y

3.6 y - 1y = 2

2.6 y = 2

y = 20/26

∴ y = 10/13

=> In the same way,

1.8 / 2+x+y = 1 / x+y

2 + x + y = 1.8*x + 1.8*y

2 = 0.8*x + 0.8*y

2 = 0.8*x + 8/13

0.8*x = 1.38

x = 1.38 / 0.8

x = 1.73 metre

Thus, the value of x is 1.73 m