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ser-zykov [4K]
2 years ago
9

Una torre de 28.2 m de altura esta situada a la orilla de un rio, desde lo alto del edificio el ángulo de depresión a la orilla

opuesta es de 25.2°. Calcular el ancho del río
Mathematics
1 answer:
Svet_ta [14]2 years ago
4 0

Answer:

El ancho del río es 59.9 metros.

Step-by-step explanation:

El ancho del río lo podemos calcular con la siguiente relación trigonométrica asumiendo que la torre forma un triángulo rectángulo con el río:

tan(\theta) = \frac{CO}{CA}

En donde:

CA: es el cateto adyacente = Altura de la torre = 28.2 m

CO: es el cateto opuesto = ancho del río =?

θ: es el ángulo adyacente a CA

Dado que el ángulo de depresión (25.2°) está ubicado fuera de la parte superior de la hipotenusa del triángulo que forma la torre con la orilla opuesta del río, debemos calcular el ángulo interno (θ) como sigue:

\theta = (90 - 25.2)^{\circ} = 64.8 ^{\circ}

Ahora, el ancho del río es:

CO = tan(\alpha)*CA = tan(64.8)*28.2 = 59.9 m

Por lo tanto, el ancho del río es 59.9 metros.

Espero que te sea de utilidad!                  

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