A person whose eyes are 1.72 m above the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor (seen below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror

x= 62.39 cm

Explanation:

Height of eyes =1.72 m

stands 2.20 m in front of a vertical plane mirror

tan θ= (H-0.38)/L

=(1.72-0.38)/2.20

=31.34°

Since, by law of reflection  

angle of incidence=angle of reflection.

Therefore, we can write  

tan(31.34)=0.38/x

0.6089 = 0.38/x

x= 0.38/0.6089

x= 0.6239 m

x= 62.39 cm

Therefore, horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror = 62.39 cm

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