 # Hypotenuse, Adjacent and Opposite Sides of a Right Triangle

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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.

### Sides of a Right Triangle

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
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)  