Shadow Lengths: Friend vs Tree

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  • Thread starter Thread starter Abdullah Qureshi
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Discussion Overview

The discussion revolves around a problem involving the lengths of shadows cast by a person and a tree at a specific time of day. Participants explore how to represent the situation diagrammatically and calculate the height of the tree based on the given shadow lengths. The scope includes mathematical reasoning and conceptual clarification related to similar triangles.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant presents the problem of determining the height of a tree based on the lengths of shadows cast by a 5 ft tall friend and the tree itself.
  • Another participant requests clarification on what the original poster has attempted and where they are encountering difficulties, emphasizing the need for specific details to provide assistance.
  • Several participants express frustration regarding the lack of initial effort shown by the original poster and suggest basic steps for drawing the diagram and understanding the problem.
  • One participant explains the concept of similar triangles and how the angles of the sun's rays relate to the lengths of the shadows, indicating that this relationship is key to solving the problem.

Areas of Agreement / Disagreement

Participants generally agree on the need to draw a diagram and understand the concept of similar triangles, but there is no consensus on the original poster's level of effort or understanding of the problem.

Contextual Notes

Some participants assume that the person and the tree are standing upright, which is a necessary condition for applying the concept of similar triangles. There is also an implicit expectation for the original poster to demonstrate prior attempts at solving the problem.

Who May Find This Useful

Students seeking help with geometry problems involving shadows and similar triangles, as well as those interested in understanding the process of diagramming mathematical problems.

Abdullah Qureshi
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At certain time of day, the shadow of your friend who is 5 ft tall measures 8 ft. At

the same time, the shadow of a tree measures 28 ft. Draw a diagram to represent

the situation. How tall is the tree?
 
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Beer soaked request follows.
Abdullah Qureshi said:
At certain time of day, the shadow of your friend who is 5 ft tall measures 8 ft. At

the same time, the shadow of a tree measures 28 ft. Draw a diagram to represent

the situation. How tall is the tree?
Please show us what you have tried and exactly where you are stuck.

We can't help you if we don't where you are stuck.
 
jonah said:
Beer soaked request follows.

Please show us what you have tried and exactly where you are stuck.

We can't help you if we don't where you are stuck.
how to draw it and put the numbers
 
Beer soaked query follows.
Abdullah Qureshi said:
how to draw it and put the numbers
What did you use to type your problem?
 
The person and the tree are, I assume, standing upright. Draw one horizontal line representing the ground, a vertical line on that horizontal line representing the person, and a longer vertical line representing the tree. Did you really need to be told that?

Now draw lines from the top of each vertical line to the "ground", at the SAME ANGLE. That is the important part. That represents the sun's rays and the sun is at the same angle for person and tree. The distance from each vertical line to the the point where the "sun's rays" meet the "ground" is the length of the shadow.

Now, do you see that you have two "similar triangles"? What do you know about similar triangles?

(If you want to do well in mathematics you are going to have to have a lot more imagination than you have shown here!)
 

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