Teorema de seno

Examples

Lessons

  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!