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Law of Sines
a/sinA = b/sinB = c/sinC
Use for AAS, ASA, SSA (ambiguous case)
Ambiguous Case (SSA)
Given A, a, b: compute h = b sinA. If a < h: no triangle. If a = h: one right triangle. If h < a < b: two triangles. If a ≥ b: one triangle.
Law of Cosines
c² = a² + b² − 2ab cosC
Use for SAS and SSS
To find angle: cosC = (a²+b²−c²)/(2ab)
Area Formulas
A = (1/2)ab sinC (SAS)
Heron's: A = √[s(s−a)(s−b)(s−c)], s=(a+b+c)/2
Vectors
v = ⟨a, b⟩ | |v| = √(a²+b²) | θ = arctan(b/a)
v = |v|⟨cosθ, sinθ⟩ | Unit vector: v/|v|
u + v = ⟨a+c, b+d⟩ | kv = ⟨ka, kb⟩