Precalculus Law of Sines and Cosines Cases

Law of Sines

if ssa, aas, asa; need a side-angle pair!

Law of Cosines

sas and sss; no angle side pair!

Ambiguity

ssa only, law of sines; can work, can be two triangles, or can completely not work

Obtuse SSA

If the matched side is longer than the unmatched side one triangle exists; if its shorter or equal no triangle exists; no ambiguity with obtuse!!!

Acute SSA (ambiguous)

If matched side is shorter than altitude, no triangle; if matched side is equal to altitude, one right triangle; if matched side is longer than altitude but shorter than unmatched side, two triangles exist; if the matched side is longer than the unmatched side, one triangle;
Have to find both angles and side lengths if ambiguous!