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# Adjacent Side (Triangle)|Definition & Meaning

## Definition

The “**adjacent**” side of a triangle is the side that is directly next to a given angle of that triangle. Generally adjacent side is the side that touches the given angle. But in right angle triangle the hypotenuse is the side that is the longest side and the side that is “**opposite**” to the hypotenuse is directly across from the given angle is **adjacent side** of that triangle.

**What Is the Adjacent Side of a Triangle? **

The **adjacent** means next to so the side which is next to the given angle is the adjacent side. The side that is perpendicular to the right angle is always considered to be the **hypotenuse**. In a right triangle, this is the side that is the longest. The terms “**opposite**” and “**adjacent**” are used to refer to the two remaining sides. The names of these sides are derived from their relationships to certain angles. The side which is opposite to the hypotenuse is adjacent.

Figure 1 – The right angle triangle with the angle between adjacent and hypotenuse side

## Detailed Explanation

Here in this article, you will find a detailed explanation of the sides of triangles mainly adjacent sides with examples for better understanding. The study of **trigonometry** and every other type of polygon can be broken down into triangles. Therefore, trigonometry emerges as an essential component of the overall subject of plane geometry. The understanding of the sides and angles of triangle is of great importance to analyzing different types of triangles.

### Sides of Right Angle Triangle

There are **three sides** to the triangle

- Adjacent
- Hypotenuse
- Opposite

The right triangle’s three sides’ relationship to one another is the subject of Pythagoras’ Theorem. According to **Pythagoras**‘ theorem, the hypotenuse square is equivalent to the sum of its other two sides. The triangle has three sides which are connected end to end with each other.

The **hypotenuse** is the side that is the longest in a right triangle. A side that is “**opposite**” is the side that is direct across from the given angle and that is the **adjacent** side. The hypotenuse, the opposite, and the adjacent are the three sides that a triangle has and the three angles that make a triangle.

The trigonometric functions have this as their foundation.

Cos(θ) = opposite/hypotenuse

Sin (θ) = **adjacent**/hypotenuse

Tan(θ) = **adjacent**/opposite

Csc(θ) = hypotenuse/**adjacent**

Sec(θ) = hypotenuse/opposite

Cot(θ) = opposite/**adjacent**

These are all the trigonometric functions in which the sides are considered. Without knowledge of the sides of a triangle, trigonometry will not be solved.

**Visualizing Adjacent Sides in Triangles**

For understanding trigonometric functions and geometry the sides and the angle concepts must be clear. A triangle with a right-angled is one that has **three** angles and **three** sides.

The right angle is the angle that is **perpendicular** to an **adjacent side**. The longest side of a right-angled triangle, which is the side that is opposite the right angle, is called the **hypotenuse**. The side in between the angle concerned and the right angle is referred to as the neighboring side or **adjacent** side. The angle in concern is opposite the opposite side or perpendicular.

In a right-angle triangle, the side which is facing the right angle is always **hypotenuse **however the remaining two sides are either **adjacent **or **opposite**. It depends on the relationship between the angle and the sides.

The figure above is the second type of triangle in this right-angle triangle there are three sides **AB**, **BC,** and **CA**. The angle **θ** is between sides **BC** and **CA**. The longest shown side is the hypotenuse which is side **CA**, opposite to the hypotenuse is the opposite side which is named **AB** and the adjacent side is the side that is exactly connected with the angle **θ** and the hypotenuse which is called side **BC**.

The above triangle is the third type of triangle. The triangle is measured as **ABC**, there are three sides named as **AB**, **BC,** and **CA**. The angle is present between side **AB** and **AC**. In another way the angle is in between two sides one is the longest side which is always **hypotenuse** and the other with the angle must be **adjacent**. The angle in this triangle is between two **adjacent** sides.

Here is another type of triangle which is a bit different than the above-explained triangles. In the above triangle, there are the same three sides but non of them is at the right angle. The triangle is named **ABC** the angle is with side **AB** and **AD** so the adjacent side is exactly with the angle shown, as this is not a right triangle so instead of hypotenuse there will be two adjacent sides. Above is a detailed explanation of three different angles’ positions so the sides will also be different, the name of the sides depends upon the position of a given angle.

## Example

Here is an example of the sides of a triangle which will help in understanding further the terminologies and the concepts of the sides as well as angles of a triangle. Identify the side that is **adjacent** to the **∠****θ**, the side **opposite** to **∠****θ, **and the **hypotenuse** of the right triangle **△****ABC** in the given diagram.

### Solution

The length of side **AB** which is hypotenuse is **13cm**, and the length of the opposite side which is measured as **AC** is **12 cm** whereas the length of the adjacent side which is with the angle is **5cm**. Now, step-by-step explanations of the sides of triangle are explained below for better analysis.

**Step 1:** Have a look at the right angle triangle and identify the right angle, the side **BC** and **AC** are making an angle of **90° ** with each other as they are perpendicular to each other so this angle is the right angle on the side opposite to right angle is the **hypotenuse**.

Thus **AB** is **hypotenuse**.

**Step 2:** Determine the angle to the respect of which the opposing are requested. The opposing side will be the side that is perpendicular to that angle.

The side opposite of **∠****B** is **AC** which is the **opposite** side.

**Step 3: **Find the side, other than the hypotenuse, that side is adjacent to that given angle. That side will be to the side.

Thus **DE** is the **adjacent** side of this triangle.

*Images/mathematical drawings are created with GeoGebra.*