If I have a triangle that has sides that are labeled x, y and z, with no square sign in the corners, so I know it is not a right triangle OR an equilateral one, and trying to compare A. x+y and B. z, then how do I figure this out?
Triangle Issue with comparing A.& B.
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geometry
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1Shortest path between two points is $\cdots\;$ – 2017-02-08
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0Is there an acute or obtuse angle opposite the side of length $z$, and do you know the **Law of Cosine**? – 2017-02-08
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0I knew that sine and tangent are related to triangles in the same way, but not sure what that title is meant to approach by itself. Out of any triangle, there is always an obtuse angle, because that is on the inside. My struggle now is trying to determine if the last inside angle IS obtuse or not. Thank you – 2017-02-08
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0Actually sorry I am not sure if that is valid what I said about obtuse angles within a triangle. Do you call that symbol Beta? It doesn't look exactly Greek, but more German. – 2017-02-08
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0@DavidThurber Lookup the [triangle inequality](https://en.wikipedia.org/wiki/Triangle_inequality). – 2017-02-08
1 Answers
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The Law of the Cosine states that if there were an interior angle of size $\beta$ opposite the side of length $z$, then :
$z^2= x^2+y^2-2xy\cos\beta$.