Adjacent Side
The adjacent side in a right triangle is the side that forms the reference angle alongside the hypotenuse.
Definition
The adjacent side is the side of a right triangle that sits right next to the angle you are looking at, forming that angle together with the hypotenuse. It appears in the cosine ratio, $\cos(\theta) = \text{adjacent}/\text{hypotenuse}$, and in the tangent ratio, $\tan(\theta) = \text{opposite}/\text{adjacent}$. On the unit circle, the adjacent side of the reference triangle equals the $x$-coordinate of the terminal point, $\cos(\theta)$, the horizontal projection of the unit radius onto the $x$-axis that defines the cosine function for all real angles.
Example
Imagine standing at a corner of a right triangle: the floor running from your feet toward the right-angle corner is the adjacent side. For a $60^\circ$ angle in a $30$-$60$-$90$ triangle with hypotenuse $2$, the adjacent side $= 2 \times \cos(60^\circ) = 2 \times 0.5 = 1$; for $\theta = 2\pi/3$ ($120^\circ$), the adjacent side of the reference triangle is $-1/2$, confirming $\cos(120^\circ) = -1/2$ via the $x$-coordinate interpretation.
Key Insight
"Adjacent" means "next to": it sits right beside your angle, while the opposite side is far across the triangle. The adjacent side shrinks as the angle grows toward $90^\circ$, which is why $\cos(90^\circ) = 0$, and this same $x$-coordinate interpretation connects directly to dot products: the dot product of two unit vectors equals $\cos(\theta)$, the cosine of the angle between them, a relationship that generalizes to $n$-dimensional Euclidean space.