# Hypotenuse, Adjacent And Opposite Sides Of A Right Triangle

### 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