Three Known Sides (SSS)

Cosine Rule
a² = b² + c² - 2bc cos(α)
α = acos((c² + b² - a²) / (2bc))

Sine Rule
h/sin(α) = b/sin(90°)
h = b sin(α)

Executive Summary
h = b sin(acos((c² + b² - a²) / (2bc)))