The law of sines and law of cosines

Used to solve oblique triangles

You can solve any oblique triangle as long as you know three pieces of information, and one thing you know is a side length.

SAA or ASA - use A+B+C=180° and the law of sines
SAS or SSS - law of cosines and sines, then A+B+C=180°
SSA (ambiguous case) - law of sines and A+B+C=180°. If two triangles exist solve both of them

Law of sines

Given a triangle with vertices A, B, and C where side a is opposite angle A and so on,

The law of sines says

a/sinA = b/sinB = c/sinC

and, equivalent

sinA/a = sinB/b = sinC/c

Law of cosines

Given a triangle with vertices A, B, and C where side a is opposite angle A and so on,

The law of cosines says

c^2 = a^2 + b^2 - 2ab * cosC
b^2 = a^2 + c^2 - 2ac * cosB
a^2 = b^2 + c^2 - 2bc * cosA

Area of oblique triangles

Law of sines for the area of a triangle

The area of a triangle equals

1/2ab * sinC

or 1/2ac * sinB

or 1/2bc * sinA

Heron's formula

Area = sqt(s(s-a)(s-b)(s-c))

where s = 1/2(a+b+c)