# Trigonometric Ratio: Tangent

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

## Definition

Tangent is the ratio of a right triangle's

(Opposite side) / (Adjacent side).**TOA**:**T**angent = (**O**pposite) / (**A**djacent)

## Meaning

Tangent means 'slope'.

Compare tangent with the slope of a line.

Both ratios mean

(vertical change, blue) / (horizontal change, purple).

## Example 1

Tangent: **TOA**.

So **t**an *A* = (**O**pposite side, 3) / (**A**djacent side, 4).

## Example 2

Tangent: **TOA**.

So **t**an *A* = (**O**pposite side, 12) / (**A**djacent side, 5).

## Example 3

Tangent: **TOA**.

So **t**an *A* = (**O**pposite side, *x*) / (**A**djacent side, 10) = 12/5.