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Word Trig Problem on Health/Medicine topic

  • #1

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

Answers and Replies

  • #2
SteamKing
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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.
 
  • #3
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
 
  • #4
SteamKing
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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?
 
  • #5
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.
 
  • #6
NascentOxygen
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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.
 
  • #7
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.
 
  • #8
NascentOxygen
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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.)
 
  • #9
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
NascentOxygen
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1.03125 X 4 = 8.25
The equals sign should separate expressions which are really, truly equal.
 
  • #11
The equals sign should separate expressions which are really, truly equal.
Ok. But that's not the right answer.
 
  • #12
NascentOxygen
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What is the right answer? The phrasing was a little ambiguous, though I believed I had figured it out.
 
  • #13
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

  • #14
NascentOxygen
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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
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
NascentOxygen
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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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