His eyes are 1.76 m above the floor, and the top of his head is 0.15 m higher. Find the height (in m) 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.
2 answers:
Answer:
Bottom of mirror to ground = 0.88m
Top of mirror to ground = 1.835m
Explanation:
From the image attached;
- A D is the distance between his eyes and the ground which is 1.76m
- A F is the distance between his eyes and the top of his head which is 0.15
-G D is the distance from the top of the mirror to the ground
-B D is distance from the bottom of mirror to the ground
From law of refraction, θi = θr and from trigonometric ratios, we can say that;
A B/B C = B D/B C
Thus, BC will cancel out and we have;
A B = B D
Now, from the diagram,
A D = A B + B D
Thus, since A B = B D
A D = B D + B D = 2B D
From the question, A D = 1.76,Thus
B D = A D/2 = 1.76/2 = 0.88m
Now,for the top of the mirror;
G D = G B + B D
As said before From law of refraction, θi = θr and from trigonometric ratios, we can say that;
G A/G E = G F/G E
G E will cancel out and we have;
G A = G F
Now, from the diagram, A F = G F + G A
Now we already know A F = 0.15m and since G A = G F,
Thus, 0.15 = G A + G A = 2G A
G A = 0.15/2 = 0.075m
From the diagram, G A + A D will give us the height of the top of the mirror above the ground.
Thus,
G D = G A + A D = 0.075 + 1.76 = 1.835m
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