# Cosine: in a Right Triangle

How to find cosine in a right triangle (trigonometry): formula, 3 examples, and their solutions.

## Formula

### Formula

Cosine is the ratio of

[Adjacent side]/[Hypotenuse]

in a right triangle.

The adjacent side means

the side adjancent to ∠A

(which is not the hypotenuse).

To remember the ratio,

remember CAH:

Cosine, Adjacent side, and Hypotenuse.

## Example 1

### Example

### Solution

Cosine is CAH:

Cosine, Adjacent side, and Hypotenuse.

The Adjacent side is 4.

The Hypotenuse is 5.

So,

C, cos A

is equal to,

A: adjacent side, 4

over,

H: hypotenuse, 5.

So cos A = 4/5.

## Example 2

### Example

### Solution

Cosine is CAH:

Cosine, Adjacent side, and Hypotenuse.

The Adjacent side is 5.

The Hypotenuse is 13.

So,

C, cos A

is equal to,

A: adjacent side, 5

over,

H: hypotenuse, 13.

So cos A = 5/13.

## Example 3

### Example

### Solution

First, find cos A

from the given right triangle.

Cosine is CAH:

Cosine, Adjacent side, and Hypotenuse.

The Adjacent side is 6.

The Hypotenuse is x.

So,

C, cos A

is equal to,

A: adjacent side, 6

over,

H: hypotenuse, x.

Next, it says

cos A = 3/5.

So write

[ = 3/5].

So cos A = 6/x = 3/5.

Solve 6/x = 3/5.

Then 3x = 30.

Divide both sides by 10.

Then x = 10.

So x = 10.