Optimizing Ladder Length for Fence-to-Pole Reach

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Homework Help Overview

The problem involves determining the shortest ladder length that can reach over an eight-foot fence to a telephone pole located one foot away. The context is rooted in geometry and optimization, likely involving principles of similar triangles and the Pythagorean theorem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to formulate the problem mathematically, noting a lack of a clear equation to start with. Some participants suggest drawing a diagram and labeling known and unknown distances with variables. They propose using similar triangles to relate the variables and derive an equation for the ladder length.

Discussion Status

Some participants have provided guidance on how to approach the problem by suggesting the use of similar triangles and variable labeling. The original poster indicates satisfaction with the assistance received, implying a productive direction has been established.

Contextual Notes

The original poster mentions confusion stemming from their initial drawing, which may have impacted their understanding of the problem setup.

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Homework Statement


An eight-foot fence stands on level ground is one foot from a telephone pole. Find the shortest ladder that will reach over the fence to the pole.


Homework Equations



Pythagoras?
Derivative.

The Attempt at a Solution


The problem is I don't know how to start this equation due to the fact that it does not have an equation to work with. You see, I'm used to seeing an equation with these kind of question then all I have to do is get the Pythagoras of the picture (telephone pole to the over the fence). Then after that I eliminate 1 variable from the 2 variable equation then use the resulting equation to get its derivative. From the derivative, I can get an x or y value depending on which I had eliminated first from the previous step before getting the derivative. Then plug that in from my original equation and get a point.

PLEASE HELP?
 
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You can draw a picture of the situation, yes? Now put numbers where you know the distance and label the distances you don't know with variables. I would suggest e.g. you call the height where the ladder touches the pole h and the distance to the fence x. You have two similar triangles. Can you use that to express h in terms of x? Now write an equation for the length of the ladder and maximize it in terms of the single remaining variable.
 
OH, THANK YOU!
Problem solved. =)
 
1calculus1 said:
OH, THANK YOU!
Problem solved. =)

THAT'S ALL IT TOOK?? And I thought you were confused. Well done.
 
Yeah, apparently my drawing was a mess. You can try my other question below this topic. =)
 

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