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

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Answer:


\Delta s \approx 334.545\,m

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((r)/(r+h) \right)


\theta = 2\cdot \cos^(-1)\left((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 = (4.792^(\circ))/(360^(\circ))\cdot (2\pi)\cdot (4000\,mi)


\Delta s \approx 334.545\,m

You fly a hot air balloon 3.5 miles above the ground. What is the measure of BD⌢, the-example-1
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