Teorema de seno



  1. Dado el siguiente triánguloABC\triangle ABC,
    Using law of sines to find angles and side lengths of triangles
    1. Encuentra el ángulo CC
    2. Encuentra aa

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Topic Basics
Para cualquier \triangle ABCABC,

aSen(A)\frac{a}{Sen (A)} =bSen(B)=\frac{b}{Sen(B)} =csin(C)=\frac{c}{\sin(C)}

\qquad \qquad \quad Y

Sen(A)a\frac{Sen (A)}{a} =Sen(B)b=\frac{Sen(B)}{b} =Sen(C)c=\frac{Sen(C)}{c}

¡Así se puede usar uno de estos pares con el Teorema de Seno para resolver problemas!

Caso ambiguo:
El caso ambiguo del Teorema de Seno proviene del caso LLA (lado-lado-ángulo).

  • Paso 1: Utiliza el ángulo en cuestión para encontrar la altura del triángulo: h=bsin(A)h=bsin(A)

  • Paso 2: Revisa si,

    Lado aa < hh, \qquad entonces no triángulos
    Lado aa = hh, \qquad entonces 1 triángulo
    Lado aa > hh, \qquad entonces 1 triángulo
    hh < Lado aa < Lado bb, \qquad entonces 2 triángulos

  • Paso 3: ¡Resuelve los triángulos!