Socratic TriangulaSean

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SOHCAHTOA

sin θ = Opposite / Hypotenuse

cos θ = Adjacent / Hypotenuse

tan θ = Opposite / Adjacent

Inverse Trig

θ = sin⁻¹(opp/hyp)

θ = cos⁻¹(adj/hyp)

θ = tan⁻¹(opp/adj)

Law of Sines

a/sin A = b/sin B = c/sin C

Law of Cosines

c² = a² + b² − 2ab·cos(C)

cos C = (a²+b²−c²) / 2ab

Pythagorean Theorem

a² + b² = c²

Angle Sum

A + B + C = 180°

Special Angles

θ

sin

cos

tan

0°

0

1

0

30°

½

√3/2

1/√3

45°

√2/2

1

60°

√3/2

½

√3

90°

1

0

—

SSA Ambiguous Case

h = b·sin(A)

a < h → 0 solutions

a = h → 1 solution (right △)

h < a < b → 2 solutions

a ≥ b → 1 solution

Pythagorean Triples

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