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If you have a right triangle and both the opposite and adjacent sides have values of ex.10 or the same value. How do you determine which side is the opposite and which is the adjacent if they are both the same length?

For example, are the opposite and adjacent parts of the triangle changed if your flip the triangle another direction? I guess what I'm asking is are the opposite and adjacent parts of the triangle the same no matter what direction it's pointing?

I'm having trouble understating how to identify the different parts of a right triangle.

Jessica M.
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The terms "opposite" and "adjacent" are relative terms, which depend on a chosen one of the two non-right angles in a right triangle. So if the triangle is $ABC$ with the right angle at vertex $C$, then if you are considering nonright angle/vertex $A$, its opposite is the side not containing that vertex, so is side $BC$, while its adjacent is the other nonhypotenuse side $AC$ which does contain the considered vertex $A$.

Basically however the triangle is oriented, one imagines "standing" inside one of the angles, and looking "across" to the "opposite" (nonhypotenuse) for that angle, and the "adjacent" for that angle is the (nonhypotenuse) side one could touch from the place one is standing.

Note that neither opposite nor adjacent is ever the hypotenuse. And as Gerry Myerson just noted in a comment, the two could have the same length or not, and the terms still distinguish which is called which, based on the chosen non-right angle.

coffeemath
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    Also note that which one is "opposite" and which one is "adjacent" has nothing whatever to do with which one is longer. – Gerry Myerson Feb 10 '14 at 08:31
  • @GerryMyerson Thanks for the note, will include in answer (with reference). – coffeemath Feb 10 '14 at 08:48
  • @coffeemath Thank you very much. So to make sure I completely understand the concept, is it correct to say there is no "fixed" adjacent and opposite sides of a right triangle? The adjacent and opposite sides of the triangle depend on which vertex you're working on? So in your example if I was considering non-right angle vertex B instead of vertex A the opposite side would be side AC and the adjacent would be BC? Is that correct? Thanks. – Jessica M. Feb 11 '14 at 01:47
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    @JessicaM. That's right. It's a relative concept, having meaning only once a particular vertex/angle is selected. And your statements in the comment above about selecting vertex B instead of A are correct. – coffeemath Feb 11 '14 at 01:52