Mirror Size & Height: Solving the Puzzle

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SUMMARY

The discussion focuses on determining the minimum size and optimal height for a mirror that allows a woman, 1.75m tall with her eyes positioned 10cm below the top of her head, to see her entire reflection. The calculations indicate that the mirror must extend 5cm above her eye level and reach 1.65m below her eyes to accommodate her full height. The solution involves applying the principles of similar triangles to derive the necessary equations for the mirror's dimensions and placement.

PREREQUISITES
  • Understanding of basic geometry and similar triangles
  • Familiarity with height measurement concepts
  • Ability to visualize and interpret geometric relationships
  • Basic algebra for equation formulation
NEXT STEPS
  • Study the properties of similar triangles in geometry
  • Learn how to apply geometric principles to real-world problems
  • Explore methods for calculating optimal dimensions in design scenarios
  • Investigate the use of graphical representations in problem-solving
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Mathematicians, architects, interior designers, and anyone involved in spatial design or visual representation will benefit from this discussion.

Icheb
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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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