# Question # To determine:To find:The height of the wall of the Warehouse. Given: The height of the eye of a person above the floor is 5 1/2 ft and the distance between person and mirror is 2 1/2 ft.

Similarity
ANSWERED To determine:To find:The height of the wall of the Warehouse.
Given:
The height of the eye of a person above the floor is $$\displaystyle{5}\frac{{1}}{{2}}$$ ft and the distance between person and mirror is $$\displaystyle{2}\frac{{1}}{{2}}$$ ft. 2020-12-01

Calculation:
From the figure, it is noticed that two similar triangles formed due to height of a person and his distance from mirror with the height of the wall and its distance from mirror.
In order to find the height of a wall, it is enough to implement the similarity definition on the triangles.
Thats, the similar triangles obey the proportionality of the corresponding length of the sides of the triangles each other.
Hence, from the given triangles the proportionality of the length of the sides is,
$$\displaystyle\frac{{{T}{B}}}{{{H}{F}}}=\frac{{{M}{B}}}{{{F}{M}}}{\left\langle'\le{t}{h}{e}\ {h}{e}{i}{g}{h}{t}\ {o}{f}\ {w}{a}{l}{l}={x}\right)}$$
$$\displaystyle\frac{{x}}{{5.5}}=\frac{{20}}{{2.5}}$$
$$\displaystyle{x}=\frac{{{\left({20}\right)}{\left({5.5}\right)}}}{{{2.5}}}$$
x=44ft
Thus, the height of the wall is 44 ft.