What is the length of the red line in this geometry problem?

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Discussion Overview

The discussion revolves around a geometry problem involving a right triangle. Participants are trying to determine the length of a specific segment (the red line) given certain dimensions of the triangle, including a height of 20 feet and a base length exceeding 58 feet. The focus is on applying geometric principles, particularly the concept of similar triangles, to find the unknown length.

Discussion Character

  • Exploratory, Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant describes the problem and provides the known dimensions of the triangle, seeking assistance in finding the length of the red line.
  • Another participant suggests using similar triangles to set up a proportion involving the known heights and the unknown length, proposing a method to solve for the unknown distance.
  • A different participant expresses confusion regarding the application of the Pythagorean theorem, indicating difficulty with the calculations and questioning their approach.
  • In response, a participant reiterates the use of similar triangles, emphasizing that the triangles share angles and thus their sides maintain proportional relationships, suggesting this method is simpler for solving the problem.

Areas of Agreement / Disagreement

There is no consensus on the best approach to solve the problem, as some participants advocate for using similar triangles while another expresses confusion with the Pythagorean theorem. The discussion remains unresolved regarding the most effective method to find the length of the red line.

Contextual Notes

Participants have not fully clarified the assumptions behind their methods, and there are unresolved mathematical steps in the proposed solutions. The discussion is limited by the lack of a visual reference to the triangle mentioned.

Hygelac
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First off, my attached image will make things make sense. I have a triangle (with a 90 degrees corner), I know that the height is 20' and that the length is more than 58'. I need to find out what the length is to the left of the 6' height mark (trying to find the length of the red line). Can anyone help me?
 

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I'll call the distance to be found x
Use similar triangles the 20 is to the 6 as x+58 is to x. From here you can solve for x.
 
Excuse me for being dumb, but I still can't figure it out.

c^2 = 20^2 + (58+x)^2 gives me really hard to work with numbers, I don't think I'm doing it right.
 
Don't use the Pythagorean theorem, us "similar triangles". Since the two triangles, the small one on the left and the large triangle, have the same angles, they are similar and their sides have the same ratios: x/6= (58+x)/20.

That's much easier to solve!
 

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