Word Trig Problem on Health/Medicine topic

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Homework Help Overview

The discussion revolves around a word problem related to trigonometry in the context of health and medicine, specifically involving distances and field sizes in radiation treatment. Participants are attempting to establish relationships between various variables such as distances from a radiation source and dimensions of triangles formed in the problem setup.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are exploring the relationships between the distances and field sizes, questioning the setup of triangles and the use of ratios. Some are attempting to apply the concept of similar triangles, while others are clarifying the correct expressions to use in their calculations.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's approaches and questioning assumptions about the problem setup. Some guidance has been offered regarding the correct interpretation of the problem, but there is no clear consensus on the correct answer yet.

Contextual Notes

Participants note that all necessary data is provided, but there is confusion regarding the interpretation of certain variables, particularly the distance from the radiation source to the skin and its role in the triangle setup. There are also references to specific problems and answers from a textbook, indicating a reliance on external materials for validation.

Cold As Ice
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Homework Statement


Posted #39 and $41. (look at the attachment).
ds = distance from the radiation source to the skin
dt = distance from the outer layer of the skin to the targeted issue
2fs = field size of the skin
2fd = targeted field size


Homework Equations



None


The Attempt at a Solution



None. Need to establish relationship between variables.

Please help.
 

Attachments

  • 2013-01-26_151935.png
    2013-01-26_151935.png
    61.5 KB · Views: 579
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Read the explanatory paragraph on the LHS of the attachment.

All of the necessary data is given. This is a problem dealing with similar triangles.
 
SteamKing said:
Read the explanatory paragraph on the LHS of the attachment.

All of the necessary data is given. This is a problem dealing with similar triangles.

I did read the explanatory paragraph.

80^2 + 4^2 = h^2

(82.5)^2 + (fd)^2 = (h2)^2

6806.25/6400 = 1.06 (ratio of two sides)

4 x 1.06 = 4.25

But this is not right since the ds = distance from the radiation source to the skin
 
You have set the problem up wrong. You are not interested in finding the length of the hypotenuse of the triangle. You know the bases of two triangles and the height of the larger triangle. You are being asked to find the height of the smaller triangle.

How would you set up an expression to find the unknown height?
 
SteamKing said:
You have set the problem up wrong. You are not interested in finding the length of the hypotenuse of the triangle. You know the bases of two triangles and the height of the larger triangle. You are being asked to find the height of the smaller triangle.

How would you set up an expression to find the unknown height?

Well, I was not looking for a hypotenuse. I was just setting up the ratio. Well do you know how to solve this problem, because I have no clue at all.
 
Cold As Ice said:
I did read the explanatory paragraph.

80^2 + 4^2 = h^2

(82.5)^2 + (fd)^2 = (h2)^2
That's right for the triangles.
6806.25/6400 = 1.06 (ratio of two sides)
No, that's the ratio of squares of the lengths. We are not interested in squares of lengths, just the ratio of the lengths of corresponding sides of similar triangles.
 
NascentOxygen said:
That's right for the triangles.

No, that's the ratio of squares of the lengths. We are not interested in squares of lengths, just the ratio of the lengths of corresponding sides of similar triangles.
Hmm. Thanks. So then 82.5/80 = 1.03125

1.03125 X 4 = 8.25 is the field size. But that is not right because d(s) is distance from the radiation source to the skin.
 
Cold As Ice said:
Hmm. You are right. So then 82.5/80 = 1.03125

1.03125 X 4 = 8.25 is the field size
A caution is timely here. Expect to lose marks for using an equals sign where what's on each side are NOT equal. :frown:

How should you have expressed this? (Try writing it over two lines.)
 
NascentOxygen said:
A caution is timely here. Expect to lose marks for using an equals sign where what's on each side are NOT equal. :frown:

How should you have expressed this? (Try writing it over two lines.)

Wait. What sides you are saying? Can you explain in details.

Thanks
 
  • #10
1.03125 X 4 = 8.25
The equals sign should separate expressions which are really, truly equal.
 
  • #11
NascentOxygen said:
The equals sign should separate expressions which are really, truly equal.

Ok. But that's not the right answer.
 
  • #12
What is the right answer? The phrasing was a little ambiguous, though I believed I had figured it out.
 
  • #13
NascentOxygen said:
What is the right answer? The phrasing was a little ambiguous, though I believed I had figured it out.

7.8 as the book say. I don't know. Maybe it is typo?

But look we used ds as one of the sides of triangle. But that ds is the entire height according what problem say. Also look I attached now again and marked it green line.
 

Attachments

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    70.6 KB · Views: 559
  • #14
I see what you mean about ds but that is making it too complicated.

An answer of 7.8 would be the field on the skin if you take 8cm as the field of the targetted tissue (and lying 2.5cm below the surface).

What are the answers for the other parts?
 
  • #15
NascentOxygen said:
I see what you mean about ds but that is making it too complicated.

An answer of 7.8 would be the field on the skin if you take 8cm as the field of the targetted tissue (and lying 2.5cm below the surface).

What are the answers for the other parts?

For Problem #41 the answer is 4.0 cm. The book only have odd. Yes, it will make it complicated. I do not know how to solve that way then. :frown:
 
  • #16
There is no ambiguity about #41. Can you show your working for it?

Also try #40 as I have worked out the answer.
 

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