In these lessons, we will learn the names of the sides of a right triangle (hypotenuse, adjacent, opposite) and how they are used in trigonometry.

**Related Pages**

Right Triangles

Basic Trigonometry

Special Right Triangles

Types Of Triangles

More Geometry Lessons

Hypotenuse, Adjacent and Opposite Sides.

In the following right triangle PQR,

- the side PQ, which is opposite to the right angle PRQ is called the
**hypotenuse**. The hypotenuse is the longest side of the right triangle. - the side RQ is called the
**adjacent**side of angle θ. - the side PR is called the
**opposite**side of angle θ.

**Note:** The adjacent and the opposite sides depend on the angle θ.
For complementary angle of θ, the labels of the 2 sides are reversed.

**Example:**

Identify the hypotenuse, adjacent side and opposite side in the
following triangle:

a) for angle x

b) for angle y

**Solution:**

a) For angle x: AB is the hypotenuse, AC is the adjacent side , and BC is the opposite side.

b) For angle y: AB is the hypotenuse, BC is the adjacent side , and AC is the opposite side.

The following diagram show how to use SOHCAHTOA for a right triangle.

**How to identify the Opposite Sides, Adjacent Sides and Hypotenuse of a Right Triangle?**

Definition of Cos, Sin, Tan, Csc, Sec, Cot for the right triangle

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

csc x = 1/sin x = hypotenuse/opposite

sec x = 1/cos x = hypotenuse/adjacent

cot x = 1/tan x = adjacent/opposite

**Using the Sine Formula (the SOH formula)**

The first part of this video will explain the difference between the hypotenuse, adjacent and opposite sides of a right triangle. Then it shows how to use the sine formula (the SOH formula).

Sine = Opposite over the Hypotenuse

**Using the Cosine Formula (the CAH formula)**

Cosine = Adjacent over Hypotenuse

**Using the Tangent Formula (the TOA formula)**

Tangent = Opposite over Adjacent

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