# Hypotenuse, Adjacent And Opposite Sides Of A Right Triangle

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.

### SOH-CAH-TOA

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)

Using the Tangent Formula (the TOA formula)

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