Triangle Trigonometry

Solving a triangle with trigonometric theorems. Given three sides (SSS), the angles follow from the law of cosines:

$\cos\alpha=\frac{b^2+c^2-a^2}{2bc}$

and the area from Heron's formula $P=\sqrt{s(s-a)(s-b)(s-c)}$, where $s=\tfrac{a+b+c}{2}$.

Given two sides and the included angle (SAS), the third side comes from $c^2=a^2+b^2-2ab\cos\gamma$, and the area from $P=\tfrac12 ab\sin\gamma$. The calculator computes every angle, the area and the perimeter, and draws the triangle to scale.