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DIA [1.3K]
2 years ago
10

Dos personas A y B , se encuentran en la orilla de un río, separadas entre sí 200 m y en la orilla opuesta en el punto C, se enc

uentra otra persona. Los ángulos CAB= 65° y CBA = 57° .¿A que distancia de A se encuentra la persona C?. ayudaaaa porfaaaa):
Mathematics
1 answer:
Kryger [21]2 years ago
7 0

Answer:

La distancia de C con respecto a A es de 197.788 metros.

Step-by-step explanation:

A manera de imagen adjunta construimos una representación del enunciado del problema, la cual representa a un triángulo cuyos tres ángulos son conocidos y la longitud del segmento AB, medida en metros, son conocidos. Por medio de la Ley del Seno podemos calcular la longitud del segmento AC (distancia de C con respecto a A), medida en metros:

\frac{AB}{\sin C} = \frac{AC}{\sin B} (1)

Si sabemos que B = 57^{\circ}, C = 58^{\circ} y AB = 200\,m, entonces la longitud del segmento AC es:

AC = AB\cdot \left(\frac{\sin B}{\sin C} \right)

AC = (200\,m)\cdot \left(\frac{\sin 57^{\circ}}{\sin 58^{\circ}} \right)

AC = 197.788\,m

La distancia de C con respecto a A es de 197.788 metros.

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