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 Topics:

More Trigonometry Lessons
### Sides of a Right Triangle

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.

### Videos

Opposite Sides, Adjacent Sides and Hypotenuse of a Right
Triangle.

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

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 Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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