Mirror Size & Height: Solving the Puzzle

AI Thread Summary
To determine the minimum size and height for a mirror that allows a woman who is 1.75m tall to see her entire body, the top of the mirror should be positioned 5cm above her eye level, while the bottom should be at 1.65m below her eyes. Using similar triangles can help derive the necessary equations for this problem. The graphical approach is a valid method, but mathematical equations based on proportions can provide a clearer solution. The discussion emphasizes the importance of understanding mirror placement and size in relation to the viewer's height.
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There is a woman who is 1,75m tall standing in front of a mirror. Her eyes are to be 10cm below the top of her head. I have to find out how small the mirror can be so that she can still see her entire body in it and how high it has to be hanging on top of the floor.

Now I think I can solve it by drawing the problem. If I draw a line from the top of her head and from her feet of the virtual image to her eyes, the highest point of the mirror would have to be 5cm above her eyes and 1,65m/2 below her eyes. Assuming this is correct (which I'm not sure of), what equations would I use to write this down? Somehow the graphical solution is all I can come up with.
 
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You are quite right. Use similar triangles.
 

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