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  1. If a triangle has two angles (30◦ and 50◦ respectively) separated by a side of length 8, is it possible to find the lengths of the other two sides using Sine Law or Cosine Law? If not, why not? If one of those Laws makes it possible, which one and why?

First off, I am not sure what they mean by separated by side length. I have no idea how I am supposed to draw this triangle, and thus cannot answer the question.

I've tried searching google, but I can't find what they would mean there either.

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I am not sure what they mean by separated by side length.

I think that just means if the base of the triangle has length 8, then the angles of the two vertices at the end of the base are $30^\circ$ and $50^\circ$, respectively.

is it possible to find the lengths of the other two sides using Sine Law or Cosine Law?

Since the sum of all three angles must be $180^\circ$, the angle of the third vertex is $100^\circ$. You now have the angle of the vertex opposite the base (length $8$), so using the sine law, you should be able to find the lengths of the other sides.

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