**The tangent theorem** is an important relationship in trigonometry that allows us to calculate angles in a triangle if certain side ratios are known. It is closely related to the sine and cosine theorems and is often used in geometric and engineering applications. The tangent theorem is **tan(𝛼) = sin(𝛼) /** **cos(𝛼)**.

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- Enter the radian measure of the opposite cathetus and the anathema into the calculator.
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## Definition of the tangent

Before we dive into the tangent theorem, we should first remember what the tangent of an angle in a right-angled triangle is.

- The tangent (often abbreviated as "tan") of an angle is the ratio of the length of the opposite side to the adjacent side.
- Expressed mathematically: $tan(α)=GegencatheteAncathete$.

## Formulation of the tangent theorem

The tangent theorem applies to any triangle that does not necessarily have to be right-angled:

For two angles $α$ and $β$ and the opposite sides a and b, the following applies: **a / b **

## Application of the tangent theorem

To use the tangent theorem effectively, the following steps should be followed:

**Identify the known quantities:**Before applying the tangent theorem, you need to identify the known angles and side lengths in your triangle.**Rearrange the formula:**If you want to calculate an angle but you know the ratio of the side lengths, you should rearrange the formula according to the angle you are looking for.**Using a calculator:**Once you have set up the formula, you can use a calculator to calculate the tangent value and find the angle you are looking for.

## Summary

The tangent theorem provides an effective way to calculate angles in a triangle if the ratios of the opposite sides are known. With a solid basic knowledge of trigonometry and the ability to apply the theorem correctly, solving such problems becomes a simple task. However, it is important to always make sure to use the formulas correctly and to keep the context of the problem in mind.