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mel-nik [20]
3 years ago
12

You fly a hot air balloon 3.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round y

our answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)

Mathematics
1 answer:
STatiana [176]3 years ago
7 0

Answer:

\Delta s \approx 334.545\,m

Step-by-step explanation:

Let assume that Earth is a sphere, the following trigonometric diagram is constructed and presented below. The central angle is given by this inverse trigonometric equation:

\theta = 2\cdot \cos^{-1} \left(\frac{r}{r+h} \right)

\theta = 2\cdot \cos^{-1}\left(\frac{4000\,mi}{4000\,mi+3.5\,mi} \right)

\theta = 4.792^{\circ}

The distance of the portion of Earth that can be seen is:

\Delta s = \frac{4.792^{\circ}}{360^{\circ}}\cdot (2\pi)\cdot (4000\,mi)

\Delta s \approx 334.545\,m

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