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

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To prove that sina' = nsinb, the relationship sinb'/sina' = 1/n is essential, but it requires clarification on the angles involved. The discussion raises questions about the equality of angles b and b', suggesting they can only be equal if the triangle has two equal sides. Additionally, the construction of the figure and the orientation of the dashed lines forming right angles are critical for accurate interpretation. Participants seek further information about the interior vector and its role in the proof. Overall, the conversation emphasizes the need for precise geometric relationships to validate the equation.
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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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