How can we prove that sina'=nsinb using the given information and figure?

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Homework Help Overview

The discussion revolves around proving the relationship \( \sin a' = n \sin b \) using a provided figure that includes angles a, b, a', b', and a variable n. Participants are examining the implications of the given information and the geometry involved.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the relationship between angles b and b', questioning whether \( \sin b = \sin b' \) holds true and under what conditions. There is also a focus on the accuracy of the figure and the implications of the dashed lines in relation to right angles.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the relationships between the angles and the geometry of the figure. Some guidance has been offered regarding the conditions under which certain relationships may hold, but no consensus has been reached.

Contextual Notes

Participants are working with a specific figure and have noted potential discrepancies in the angles presented. There is an emphasis on understanding the geometric setup and the implications of the triangle's properties.

annalian
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Homework Statement


look at the figure and prove that sina'=nsinb. We have given a, b, a', b' and n
http://s32.postimg.org/n7rnu0khx/image.png

Homework Equations


sinb'/sina'=1/n

The Attempt at a Solution


But in the equation we have b, not b'. I made the figure. How would the correct one be?
 
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Can you prove that ##\sin b = \sin b'##?
 
RUber said:
Can you prove that ##\sin b = \sin b'##?
No, only if the triangle has 2 equal sides
 
Are the dashed lines making a and a' forming right angles with the sides of the triangle?
What other information do you have about this problem? How is the interior vector chosen/created?
 

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