====== Non-Right Triangle Trigonometry ======
Below are a few laws that help with finding sides and angles for non right triangles. We will use the standard triangle $\Delta ABC$ with sides $a$, $b$, and $c$ being opposite of their respective angles.

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===== Law of Sines =====
The law of sines is the most simple of the trig laws, however there are some edge cases you must worry about.
  * $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

When solving for an angle on an ASS((angle side side)) triange, there can be **two** solutions, and thus two triangles. To get the other angle, subtract the calculated one by //180 degrees// and check if it makes a valid triangle that doesn't have angle measures > 180. Sometimes there can also be no solution if your calculator spits out a domain error.

===== Law of Cosine =====
While the law of cosine seems difficult to remember, it is actually just Pythagorean theorem with an angle correction.
  * $c^2 = a^2 + b^2 - 2ab\cos C$
With this angle correction, you can actually swap $a$, $b$, and $c$ around solong as you keep the $c$ and $C$ angle pair of the original equation. So, the following are actually also valid:
  * $a^2 = b^2 + c^2 - 2bc\cos A$
  * $b^2 = a^2 + c^2 - 2ac\cos B$

===== Area of a Non-Right Triangle =====
FIXME check if the ASA thing is true or not.

The formula is just the standard triangle area equation with a $\sin$ added.
  * $\text{area} = \frac{1}{2}bc\sin A$
The variables can be swapped around just like in Law of Cosine, but the triangle **NEEDS** to be an ASA((angle side angle)) triangle for this to work.
==== Heron's Area Formula ====
The Law of Cosines can be used to establish the following formula for the area of a triangle. You can use it for any SSS((side side side)) triangle.
  * $\text{area} = \sqrt{s(s-a)(s-b)(s-c)}$ where $s = \frac{a + b + c}{2}$