Question

An observer is 150 meters away distance of a hot air balloon online straight line at ground level. From your position, measures an elevation angle of 40° up to the base of the balloon. At what height is find the hot air balloon?

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Answer to a math question An observer is 150 meters away distance of a hot air balloon online straight line at ground level. From your position, measures an elevation angle of 40° up to the base of the balloon. At what height is find the hot air balloon?

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Madelyn
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86 Answers
Solution:
1. Dado:
- Distancia horizontal desde el observador hasta la base del globo: d = 150 \ m
- Ángulo de elevación: \theta = 40^{\circ}

2. Usamos la función tangente para encontrar la altura h del globo aerostático. La tangente de un ángulo en un triángulo rectángulo es la razón entre la altura y la distancia horizontal:
\tan(\theta) = \frac{h}{d}

3. Sustituimos los valores conocidos en la ecuación:
\tan(40^{\circ}) = \frac{h}{150}

4. Resolvemos para h:
h = 150 \times \tan(40^{\circ})

5. Calculamos el valor numérico:
* Usando una calculadora, \tan(40^{\circ}) \approx 0.8391
* Entonces: h \approx 150 \times 0.8391 = 125.865 \ m

La altura del globo aerostático es aproximadamente 125.865 \ m.

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