A man stands in front of a mirror as shown in the figure. His eyes are 1.82 m ab

Question

A man stands in front of a mirror as shown in the figure. His eyes are 1.82 m above the floor, and the top of his head is 0.13 m higher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. top m bottom m How is the distance d from the top to the bottom of the mirror related to the man's height h? Use the symbol h to represent the man's height. d = How is the length of the mirror related to the distance from the floor to the top and bottom of the mirror? h

Explanation / Answer

for toe to eyes

((1.82))/x = bottom/x

bottom = ((1.82/2) = 0.91 m

for head to eyes

(dy/2)/x = (h-top)/x

h - top = 0.13/2 = 0.065

h = 1.82 + 0.13 = 1.95

top = h - 0.065 = 1.885 m

d = top - bottom

d = 1.885-0.91= 0.975 m

d/h = 0.975/1.95

d = 0.5*h

d = (1/2)h = h/2

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