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Aleonysh [2.5K]

2 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

1 answer:

Inga [223]2 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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