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Resuelve el triángulo ABC con la información suministrada. 1. \( \angle A=60^{\circ} \quad \& B=70^{\circ} \quad b=10 \)

Ask by Warner King. in Colombia
Mar 13,2025

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Los ángulos del triángulo ABC son 60°, 70° y 50°. Los lados miden aproximadamente 9.22, 10, y 8.16 unidades.

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Para resolver el triángulo ABC, primero podemos encontrar el tercer ángulo, \( C \), utilizando la suma de los ángulos en un triángulo, que es \( 180^{\circ} \). Así, \( C = 180^{\circ} - A - B = 180^{\circ} - 60^{\circ} - 70^{\circ} = 50^{\circ} \). Luego, podemos aplicar la ley de senos para encontrar los lados \( a \) y \( c \). Según la ley de senos: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] Sustituyendo los valores que tenemos: \[ \frac{a}{\sin(60^{\circ})} = \frac{10}{\sin(70^{\circ})} \] \[ a = 10 \cdot \frac{\sin(60^{\circ})}{\sin(70^{\circ})} \] Y para encontrar \( c \): \[ \frac{c}{\sin(50^{\circ})} = \frac{10}{\sin(70^{\circ})} \] \[ c = 10 \cdot \frac{\sin(50^{\circ})}{\sin(70^{\circ})} \] Calculando estos valores, se puede resolver el triángulo ABC completamente.

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