Explanation:
The given data is as follows.
Distance between eyes of the person from the floor, c = 1.76 m
Distance between the floor and plane mirror, d = 2.96 m
Height of bottom edge of the mirror from the ground, a = 0.54 m
Let us assume that the horizontal distance is x. According to the figure,
BC = c - a
= 1.76 m - 0.54 m
= 1.22 m
Since, the triangle ABC is similar to the triangle CDE hence,
[tex]\frac{AB}{BC} = \frac{ED}{CD}[/tex]
[tex]\frac{d}{BC} = \frac{x}{a}[/tex]
x = [tex]a \times \frac{d}{BC}[/tex]
= [tex]\frac{2.96 m}{1.22 m} \times 0.54 m[/tex]
= 1.310 m
= [tex]1.310 m \times \frac{100 cm}{1 m}[/tex]
= 131 cm
Thus, we can conclude that the horizontal distance to the base of the wall supporting the mirror of the nearest point on the floor is 131 cm.
