A tree and a mirror on the ground

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SUMMARY

The problem involves calculating the height of a tree using the principles of similar triangles, given a plane mirror on the ground. The mirror is positioned such that one end is 2.1 m from the observer and the other end is 35 m from the tree. The observer is 1.6 m tall, and the solution requires establishing a ratio between the observer's height and distance from the mirror to the tree's height and its distance from the mirror. The correct application of the similar triangles principle is crucial for deriving the tree's height accurately.

PREREQUISITES
  • Understanding of similar triangles
  • Basic knowledge of optics and reflection
  • Familiarity with height-distance ratio calculations
  • Ability to interpret geometric figures
NEXT STEPS
  • Review the principles of similar triangles in geometry
  • Study the laws of reflection in optics
  • Practice problems involving height and distance ratios
  • Examine examples of real-world applications of mirrors and reflections
USEFUL FOR

Students in physics or geometry courses, educators teaching optics, and anyone interested in practical applications of similar triangles in real-world scenarios.

sklotz
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Homework Statement



A plane mirror made of a very thin piece of glass lies flat on the ground. As shown in the following figure, one end of the mirror is 2.1 m from you and the other end is 35 m from a nearby tree. You are 1.6 m tall, and the mirror has a length L. The mirror is arranged so that you can just see the image of the top of the tree at one edge of the mirror. how tall is the tree?

Homework Equations



I know you have to use the principle of similar triangles

The Attempt at a Solution



I tried using height of person/distance of person from mirror = height of tree/distance of tree from mirror . This is similar to a problem our TA did in class and I thought I was using the correct formula, however, I have been unable to get the correct answer and I don't understand what I am doing wrong and only have one attempt left for credit
 
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Any chance you could show the figure?

What edge does he see the top of the tree? the edge that is closer to the man, or the edge that is closer to the tree?

I believe you answer will be in terms of L. Unless L has a value?
 
A figure and some hints are given on the second page of this file:
http://web.ics.purdue.edu/~jensend/media/pdf/phys221/homework/hints10.pdf

But note the numbers in the problem are different.
 

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