October 8, 2009
No CommentsAn Introduction to the Law of Tangents
Description
A detailed tutorial on the Law of Tangents. Step by step tutorial including several examples of the Law of Tangents for reference.
Overview
The Law of Tangents refers to the lengths of the three sides of a triangle and the tangents of the angles. This can be used with respect to any triangle, not just right triangles. While the Law of Tangents is not as well known as the Law of Sines or the Law of Cosines, it is useful. The Law of Tangents can be used whenever either two sides and an angle, or two angles and a side, are known on any given triangle. The proof of this law starts with the Law of Sines. The Law of Tangents is as follows:
![\frac{a-b}{a+b} = \frac{\tan[\frac{1}{2}(\alpha-\beta)]}{\tan[\frac{1}{2}(\alpha+\beta)]}.](http://s.wordpress.com/latex.php?latex=%5Cfrac%7Ba-b%7D%7Ba%2Bb%7D%20%3D%20%5Cfrac%7B%5Ctan%5B%5Cfrac%7B1%7D%7B2%7D%28%5Calpha-%5Cbeta%29%5D%7D%7B%5Ctan%5B%5Cfrac%7B1%7D%7B2%7D%28%5Calpha%2B%5Cbeta%29%5D%7D.&bg=ffffff&fg=000000&s=0 "\frac{a-b}{a+b} = \frac{\tan[\frac{1}{2}(\alpha-\beta)]}{\tan[\frac{1}{2}(\alpha+\beta)]}.")
