### 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.

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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