Answer:
[tex]h \approx 59.898\,km[/tex]
Step-by-step explanation:
El diagrama trigonométrico que representa el enunciado es incluido abajo como adjunto. Las siguientes relaciones trigonométricas describen la localización del globo. (The trigonometric diagram representing the statement is included below as attachment. The following trigonometric relations describes the location of the balloon):
[tex]\tan 27^{\circ} = \frac{h}{x}[/tex]
[tex]\tan 36^{\circ} = \frac{h}{200-x}[/tex]
A continuación, se obtiene la distancia horizontal: (The horizontal distance is obtained hereafter):
[tex]x \cdot \tan 27^{\circ} = (200-x)\cdot \tan 36^{\circ}[/tex]
[tex]x \cdot (\tan 27^{\circ} + \tan 36^{\circ})= 200\cdot \tan 36^{\circ}[/tex]
[tex]x = \frac{200\cdot \tan 36^{\circ}}{\tan 27^{\circ}+ \tan 36^{\circ}}[/tex]
[tex]x \approx 117.557\,km[/tex]
La altura aproximada del globo es (The approximated height of the globe is):
[tex]h = x\cdot \tan 27^{\circ}[/tex]
[tex]h \approx 59.898\,km[/tex]
