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Mnenie [13.5K]
3 years ago
14

✔ Desde un supermercado, se observa el ático de un rascacielos de 527 metros de altura bajo un ángulo de 42°. Calcular la distan

cia que hay desde el supermercado hasta la puerta del rascacielos. Dond✔ Desde un supermercado, se observa el ático de un rascacielos de 527 metros de altura bajo un ángulo de 42°. Calcular la distancia que hay desde el supermercado hasta la puerta del rascacielos. Desde un supermercado, se observa el ático de un rascacielos de 527 metros de altura bajo un ángulo de 42°. Calcular la distancia que hay desde el supermercado hasta la puerta del rascacielos.

Mathematics
1 answer:
Goryan [66]3 years ago
4 0

Answer:

La distancia desde el supermercado hasta la puerta del rascacielos es de 585,29 metros

Step-by-step explanation:

Dado que la altura del ático = 527 metros

El ángulo de elevación de la vista = 42 °

Tomamos la posición de la persona que ve el rascacielos en el supermercado, el ático del rascacielos y la base del rascacielos directamente frente a la persona, formando los vértices de un triángulo rectángulo ABC, respectivamente.

Por lo tanto;

AB = Línea de visión desde la persona hasta el ático.

BC = La altura del rascacielos = 527 metros

AC = La distancia desde el supermercado hasta la puerta del rascacielos.

De lo cual se nos da, ∠BAC = 42 °

Por lo tanto, ∠ACB = 90 ° y el ángulo de depresión desde el ático del rascacielos hasta la persona en el supermercado ∠ABC = 180 ° - 90 ° - 42 ° = 48 °

De la regla senoidal, tenemos;

\dfrac{BC}{sin(\angle BAC)} =\dfrac{527}{sin(42^{\circ})} = \dfrac{AC}{sin(\angle BAC))} = \dfrac{AC}{sin(48^{\circ})}

Lo que da;

AC = \dfrac{527 \times sin(48^{\circ}) }{sin(42^{\circ})}= 585.29 \ metros

Por lo tanto;

La distancia desde el supermercado hasta la puerta del rascacielos = 585,29 metros.

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