Given:
CH = 3960 miles
Altitude = 240 miles
To find:
The distance from the space station to the horizon.
Solution:
The reference image for answer is attached below.
Radius = 3960 miles
CD = CH = 3960
ED = 240
EC = CD + ED
= 3960 + 240
EC = 4200 miles
By Pythagorean theorem:
[tex]E C^{2}=E H^{2}+C H^{2}[/tex]
[tex]4200^{2}=E H^{2}+3960^{2}[/tex]
[tex]17640000=E H^{2}+15681600[/tex]
Subtract 15681600 from both sides.
[tex]17640000-15681600=E H^{2}+15681600-15681600[/tex]
[tex]1958400=E H^{2}[/tex]
Taking square root on both sides, we get
[tex]$1399.428=EH[/tex]
[tex]$1400 \approx EH[/tex]
The distance from space station to the horizon is approximately 1400 miles.
