Laws of Sines and Cosines Flashcards

Grade 10 · Math · Flashcards

Formulas, cases, and strategies for solving non-right triangles.

Flashcards

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines: c² = a² + b² - 2ab·cos(C)
Law of Cosines to find angle: cos(C) = (a² + b² - c²) / (2ab)
When to use Law of Sines: When you have a side paired with its opposite angle: AAS, ASA, or SSA
When to use Law of Cosines: When you have SAS or SSS — no side-angle pair available
AAS: Two angles and a non-included side → Law of Sines
ASA: Two angles and the included side → Law of Sines
SAS: Two sides and the included angle → Law of Cosines
SSS: All three sides known → Law of Cosines to find an angle
SSA (Ambiguous Case): Two sides and non-included angle; may give 0, 1, or 2 valid triangles
Law of Cosines connection to Pythagorean theorem: When C=90°, cos(C)=0 so c²=a²+b²; the Pythagorean theorem is a special case
Solving a triangle: Finding all 3 sides and all 3 angles; remember A+B+C=180°
Height in ambiguous case: h = b·sin(A); if a < h: 0 triangles; if a = h: 1; if h < a < b: 2; if a ≥ b: 1