**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Law of tangents

Summary

In trigonometry, the law of tangents or tangent rule is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.
In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and γ are the angles opposite those three respective sides. The law of tangents states that
:
\frac{a-b}{a+b}
= \frac{\tan\tfrac12(\alpha-\beta)}
{\tan\tfrac12(\alpha+\beta)}.
The law of tangents, although not as commonly known as the law of sines or the law of cosines, is equivalent to the law of sines, and can be used in any case where two sides and the included angle, or two angles and a side, are known.
Proof
To prove the law of tangents one can start with the law of sines:
: \frac{a}{\sin\alpha} = \frac{b}{\sin\beta}.
Let
: d = \frac{a}{\sin\alpha} = \frac{b}{\sin\beta}
so that
:
a = d \sin\alpha \quad\text{and}
\quad b = d \sin\beta.
It

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications

Related people

Related courses

Related units

No results

No results

No results

No results

Related concepts

Related lectures

No results

No results