Finding the Adjacent and Opposite Sides in a Right Triangle

Date: 06/12/2008 at 20:49:13
From: D
Subject: trying to tell the difference between adjacent and opposite

What is the difference between adjacent and opposite and how do I 
find it?  I can't tell the difference but I think adjacent is across
the hypotenuse

Date: 06/12/2008 at 23:03:20
From: Doctor Peterson
Subject: Re: trying to tell the difference between adjacent and opposite

Hi, D.

In everyday usage, "adjacent" means "next to", and "opposite" means
"across from".  That is true in math as well.

In trigonometry, if you imagine yourself standing on one acute angle
of a right triangle, the two sides that meet at your corner are the
hypotenuse (the longest side, across from the right angle) and one of
the two legs.  Since that one is NEXT TO you, it is the ADJACENT leg.
There is a third side, which is ACROSS FROM you.  That is the OPPOSITE
leg.

Note that it matters which angle you are calling "yours"; you can only
say that a leg is adjacent or opposite in relation to a specific
vertex (angle).  The leg adjacent to that angle is the one that forms
part of the angle; the leg opposite to the angle is the one that
doesn't touch that vertex.

In the following pictures, I have labeled different vertices as A.  In
each case, the leg labeled "adj" is next to A, and the leg labeled
"opp" is across from A:

              +                   A
      hyp  /  |           hyp  /  |
        /     |opp          /     |adj
     /        |          /        |
  A-----------+       +-----------+
       adj                 opp

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/