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More Trigonometry Lessons

Trigonometry Games

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

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.

a) for angle x

b) for angle y

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

More Trigonometry Lessons

Trigonometry Games

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.

In the following right triangle PQR,

• the side PQ, which is opposite to the right angle PRQ is called the

• the side RQ is called the

• the side PR is called the

** Example: **

a) for angle x

b) for angle y

** Solution: **

b) For angle y: AB is the hypotenuse, BC is the adjacent side , and AC is the opposite side.

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

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

Cosine = Adjacent over Hypotenuse

Tangent = Opposite over Adjacent

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