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Romashka-Z-Leto [24]
3 years ago
15

dos aviones parten de una ciudad con direcciones S32°E y E57°N¿ cuál es el angulo que forma sus direcciones?​

Mathematics
1 answer:
Elan Coil [88]3 years ago
4 0

Answer:

El ángulo formado entre las dos direcciones es aproximadamente 115º.

Step-by-step explanation:

Las direcciones dadas en el enunciado significan lo siguiente:

S32ºE - <em>32º al este del sur.</em>

E57ºN - <em>57º al norte del este.</em>

Vectorialmente hablando, cada dirección es la siguiente:

S32ºE

A(x,y) = (\sin 32^{\circ}, -\cos 32^{\circ})

A(x,y) = (0.530, -0.848)

E57ºN

B(x,y) = (\cos 57^{\circ},\sin 57^{\circ})

B(x,y) = (0.545, 0.839)

El ángulo formado entre los dos vectores unitarios (\theta), medido en grado sexagesimales, puede determinarse mediante la siguiente ecuación vectorial:

\theta = \cos^{-1} \frac{A\,\bullet \,B}{\|A\|\cdot \|B\|}

Donde:

\|A\| - Norma de A(x,y).

\|B\| - Norma de B(x,y).

Si sabemos que A(x,y) = (0.530, -0.848), B(x,y) = (0.545, 0.839), \|A\| = 1 y \|B\| = 1, entonces el ángulo formado entre los dos vectores es:

\theta = \cos^{-1} \frac{(0.530)\cdot (0.545)+(-0.848)\cdot (0.839)}{(1)\cdot (1)}

\theta \approx 115^{\circ}

El ángulo formado entre las dos direcciones es aproximadamente 115º.

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