# Sine: in a Right Triangle

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

## Formula

### Formula

Sine is the ratio of

[Opposite side]/[Hypotenuse]

in a right triangle.

The opposite side means

the side opposite to ∠A.

To remember the ratio,

remember SOH:

Sine, Opposite side, and Hypotenuse.

## Example 1

### Example

### Solution

Sine is SOH:

Sine, Opposite side, and Hypotenuse.

The Opposite side is 3.

The Hypotenuse is 5.

So,

S, sin A

is equal to,

O: opposite side, 3

over,

H: hypotenuse, 5.

So sin A = 3/5.

## Example 2

### Example

### Solution

Sine is SOH:

Sine, Opposite side, and Hypotenuse.

The Opposite side is 12.

The Hypotenuse is 13.

So,

S, sin A

is equal to,

O: opposite side, 12

over,

H: hypotenuse, 13.

So sin A = 12/13.

## Example 3

### Example

### Solution

First, find sin A

from the given right triangle.

Sine is SOH:

Sine, Opposite side, and Hypotenuse.

The Opposite side is x.

The Hypotenuse is 10.

So,

S, sin A

is equal to,

O: opposite side, x

over,

H: hypotenuse, 10.

Next, it says

sin A = 4/5.

So write

[ = 4/5].

So sin A = x/10 = 4/5.

Solve x/10 = 4/5.

Multiply 10 to both sides.

Then x = [4/5]⋅10.

Cancel the denominator 5

and reduce the numerator 10 to, 10/5, 2.

4⋅2 = 8

So x = 8.