Word Trig Problem on Health/Medicine topic

[Cold As Ice]

Homework Statement

Posted #39 and $41. (look at the attachment).
d_s = distance from the radiation source to the skin
d_t = distance from the outer layer of the skin to the targeted issue
2f_s = field size of the skin
2f_d = targeted field size

Homework Equations

None

The Attempt at a Solution

None. Need to establish relationship between variables.

Please help.

 

[SteamKing]

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.

 

[Cold As Ice]

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 + (f_d)^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 d_s = distance from the radiation source to the skin

 

[SteamKing]

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?

 

[Cold As Ice]

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.

 

[NascentOxygen]

I did read the explanatory paragraph.

80^2 + 4^2 = h^2

(82.5)^2 + (f_d)^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.

 

[Cold As Ice]

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.

 

[NascentOxygen]

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.

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

 

[Cold As Ice]

A caution is timely here. Expect to lose marks for using an equals sign where what's on each side are NOT equal.

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

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

Thanks

 

[NascentOxygen]

1.03125 X 4 = 8.25

The equals sign should separate expressions which are really, truly equal.

 

[Cold As Ice]

The equals sign should separate expressions which are really, truly equal.

Ok. But that's not the right answer.

 

[NascentOxygen]

What is the right answer? The phrasing was a little ambiguous, though I believed I had figured it out.

 

[Cold As Ice]

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

 

[NascentOxygen]

I see what you mean about d_s 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?

 

[Cold As Ice]

I see what you mean about d_s 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.

 

[NascentOxygen]

There is no ambiguity about #41. Can you show your working for it?

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