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.

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More Trigonometry Lessons

### Sides of a Right Triangle

Hypotenuse, Adjacent and Opposite Sides.

In the following right triangle*PQR, *

**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.

a) for angle* x*

b) for angle *y*

*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.

**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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

More Trigonometry Lessons

In the following right triangle

- 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**.*

* Example: *

a) for angle

* Solution: *

b) For angle

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

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

Cosine = Adjacent over Hypotenuse

Tangent = Opposite over Adjacent

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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