Calculadora de Triángulo LLA

Paso 1: Ingresa las dos longitudes de lado conocidas (a y b) y el ángulo conocido A (opuesto al lado a). Paso 2: Haz clic en Calcular. Paso 3: La calculadora determina cuántas soluciones existen (0, 1 o 2) y muestra todos los triángulos válidos con todos los lados y ángulos. Paso 4: Revisa el análisis del caso ambiguo.

Dados los lados a, b y el ángulo A (opuesto a a), aplica la Ley de Senos: sin(B)/b = sin(A)/a → sin(B) = b×sin(A)/a. Si sin(B) > 1: ninguna solución. Si sin(B) = 1: un triángulo rectángulo. Si sin(B) < 1: comprueba si a < b — si es así, dos soluciones (B₁ y B₂ = 180°−B₁); si a ≥ b, una solución. Tercer ángulo C = 180°−A−B; lado c = a×sin(C)/sin(A).

The SSA (Side-Side-Angle) Triangle Calculator is an essential mathematical tool designed to help students, educators, and professionals instantly solve complex triangular geometries using the Law of Sines. While most triangle configurations (like Side-Side-Side or Side-Angle-Side) guarantee a single, unique solution, the SSA configuration is uniquely challenging because it introduces the 'ambiguous case.'

When you are given two sides and a non-included angle, the geometric constraints do not necessarily define one specific triangle. Depending on the exact measurements, the inputs can result in three different outcomes: no valid triangle can be formed (the side is too short to close the shape), exactly one unique right or oblique triangle exists, or two entirely different but equally valid triangles can be constructed. Determining which scenario applies requires manually calculating sine ratios and cross-checking angle limits.

Our straightforward calculator handles the heavy lifting by automatically detecting the ambiguous case. It instantly evaluates your inputs to determine whether zero, one, or two solutions are possible, and then calculates the complete set of missing angles and sides for every valid configuration. This makes it an invaluable resource for verifying homework, solving surveying problems, or exploring advanced trigonometry without the tedious manual calculations.