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Yuri [45]
3 years ago
9

El punto más alto de un repetidor de televisión situado en la cima de una montaña se ve desde un punto del suelo p bajo un ángul

o de 67º si nos acercamos a la montaña 30 metros lo vemos bajo un ángulo de 70º y desde ese mismo punto vemos la cima de la montañas bajo un ángulo de 66 °. Calcular la altura del repetidor.
Mathematics
1 answer:
Maksim231197 [3]3 years ago
4 0

Answer:

El repetidor tiene aproximadamente 90.494 metros de altura.

Step-by-step explanation:

Al término de esta solución podemos encontrar el diagrama geométrico con toda la información derivada de lo descrito en el enunciado de la pregunta. Aquí designamos la altura del repetidor con la letra h, medida en metros. Procedemos a resolver el modelo a partir de la Ley del Seno:

\frac{30\,m}{\sin 3^{\circ}} = \frac{s}{\sin 67^{\circ}}

s \approx 527.651\,m

\frac{s}{\sin 156^{\circ}} = \frac{h}{\sin 4^{\circ}}

h \approx 90.494\,m

El repetidor tiene aproximadamente 90.494 metros de altura.

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