# Trigonometric Ratio: Sine

How to solve sine (trigonometric ratio) problems: definition, examples, and their solutions.

## Definition

Sine is the ratio of a right triangle's

(Opposite side) / (Hypotenuse).**SOH**:**S**ine = (**O**pposite) / (**H**ypotenuse)

Trigonometric ratios can be used

to express the shape of a triangle.

Instead of drawing the picture

or writing all the sides and angles of a triangle,

you can write 'sin *A* = '

to show the ratio of (opposite side)/(hypotenuse),

which shows the shape of a triangle.

## Example 1

Sine: **SOH**.

So **s**in *A* = (**O**pposite side, 3) / (**H**ypotenuse, 5).

## Example 2

Sine: **SOH**.

So **s**in *A* = (**O**pposite side, 12) / (**H**ypotenuse, 13).

## Example 3

Sine: **SOH**.

So **s**in *A* = (**O**pposite side, *x*) / (**H**ypotenuse, 10) = 4/5.