Law of Sines, Law of Cosines, and Area of Oblique Triangles

Area Formula #1

A=\frac12ab\sin\left(C\right)

Area Formula #2

A=\frac12ac\sin\left(B\right)

Area Formula #3

A=\frac12bc\sin\left(A\right)

Heron’s Formula

\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}

Law of Cosines Equation #1

b^2+c^2-2bc\cos\left(A\right)

Law of Cosines Equation #2

b^2=a^2+c^2-2ac\cos\left(B\right)

Law of Cosines Equation #3

c^2=a^2+b^2-2ab\cos\left(C\right)

Law of Sines

\frac{\sin\left(A\right)}{a}=\frac{\sin\left(B\right)}{b}=\frac{\sin\left(C\right)}{c}