Answer:
[tex]\Delta s \approx 334.545\,m[/tex]
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:
[tex]\theta = 2\cdot \cos^{-1} \left(\frac{r}{r+h} \right)[/tex]
[tex]\theta = 2\cdot \cos^{-1}\left(\frac{4000\,mi}{4000\,mi+3.5\,mi} \right)[/tex]
[tex]\theta = 4.792^{\circ}[/tex]
The distance of the portion of Earth that can be seen is:
[tex]\Delta s = \frac{4.792^{\circ}}{360^{\circ}}\cdot (2\pi)\cdot (4000\,mi)[/tex]
[tex]\Delta s \approx 334.545\,m[/tex]
