Adjacent side

Definition

An adjacent side in a right triangle is one of the two sides that form the right angle. It specifically refers to the side that is next to a given angle, excluding the hypotenuse.

5 Must Know Facts For Your Next Test

1. The adjacent side is never the hypotenuse; it is one of the legs forming the right angle.
2. In trigonometric functions, cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.
3. For angle $\theta$, if $a$ is the adjacent side and $c$ is the hypotenuse, then $a = c \cdot \cos(\theta)$.
4. The length of an adjacent side varies depending on which acute angle in a right triangle you are considering.
5. In coordinate geometry, for a point $(x,y)$ on a unit circle, $x$ represents the length of the adjacent side when interpreting cosine.

Review Questions

• How do you identify which side is adjacent to a given angle in a right triangle?
• What is the relationship between an adjacent side and cosine in trigonometry?
• If you know an angle and its hypotenuse in a right triangle, how can you find its adjacent side?

Related terms

Opposite Side: In a right triangle, it is the side opposite to a given angle.

Hypotenuse: The longest side in a right triangle, opposite the right angle.

$\cos(\theta)$: $\cos(\theta)$ represents cosine function which equals to $\frac{\text{adjacent}}{\text{hypotenuse}}$.