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Aleonysh [2.5K]
3 years ago
13

Un guardia forestal divisa, desde un punto de observación A, un incendio en la dirección N27° 10’ E. Otro guardia, que se encuen

tra en el punto de observación B, a 6 millas al este de A, ve el mismo fuego en la dirección N52° 40’ W. Calcula, al décimo de milla más cercano la distancia de cada uno de los puntos de observación al incendio

Mathematics
1 answer:
Inga [223]3 years ago
8 0

Answer:

la distancia del punto de observación A al incendio = 5.5 millas

la distancia del punto de observación B al incendio = 3.8 millas

Step-by-step explanation:

La expresión esquemática de la pregunta se puede ver en la imagen adjunta a continuación :

Del siguiente diagrama;

Usando la sine regla:

\dfrac{sin \  F}{f} = \dfrac{sin  \ A }{a}

\dfrac{sIn \  79}{6} = \dfrac{sin \   63}{a}

a sin 79 = 6 sin 63

a =\dfrac{6 \times sin \ 63}{sin \ 79}

a =\dfrac{6 \times 0.8910}{0.9816}

a = 5.446 millas

la distancia del punto de observación A al incendio = 5.5 millas (a la décima más cercana)

\dfrac{sin \  F}{f} = \dfrac{sin  \ B}{b}

\dfrac{sin \  79}{6} = \dfrac{sin  \ 38}{b}

b sin 79 = 6 sin 38

b  = \dfrac{6 \times sin  \ 38}{sin \  79}

b  = \dfrac{6 \times0.6157 }{0.9816}

b = 3.7635 millas

la distancia del punto de observación B al incendio = 3.8 millas (a la décima más cercana)

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