Question

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.)

Answer 1

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:

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

$\Delta s \approx 334.545\,m$