Naming the Sides of a Right-Angled Triangle
Examine the right triangle shown below. We want to assign each side one of three names: opposite, adjacent, and hypotenuse.
In this triangle, we have identified an angle of interest by giving it a variable name. (In this case we named it x, but other common angle variables are θ (theta) and α (alpha)). You choose which angle is 'of interest' depending on what the question is asking for. You will see this in later examples.
To name the sides of the triangle, it is usually easiest to start with the hypotenuse. be skilled at locating the hypotenuse. The same triangle is shown below with the hypotenuse labelled.
Now we must label the other two sides. The two labels that we will use are opposite and adjacent. It is usually easiest to label the opposite side first. The rule is this:
The opposite side (usually labelled opp or simply o) is found opposite the 'angle of interest'.
To find which side is opposite any given angle, find the side that does not touch that angle. The same triangle is pictured again below with the opposite side labelled.
The last side to label is the adjacent side. If you have already labelled the hypotenuse and the opposite side, the adjacent side is the only side left without a name. However, the definition to determine which side is the adjacent side is given below:
The adjacent side (usually labelled adj or simply a) is the side that 'touches' the 'angle of interest' that is NOT the hypotenuse.
Our familiar triangle is shown below with all three sides properly labelled.
To further our exploration, let's see what happens if we pick the other unknown angle as our angle of interest. Examine the diagram below:
As you can see, if we name the other angle x, the old adjacent side becomes the opposite side and the old adjacent side becomes the opposite side. The hypotenuse is ALWAYS the hypotenuse.
So, two rules to follow:
- You CANNOT give the names opposite and adjacent to sides of a triangle until you have identified an 'angle of interest'.
- You can only use these names (and ratios) with right-angled triangles.
Now that you have read through all of this, you can try some questions, or return to the first page.