Question

Question

Answer 1

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:

$E C^{2}=E H^{2}+C H^{2}$

$4200^{2}=E H^{2}+3960^{2}$

$17640000=E H^{2}+15681600$

Subtract 15681600 from both sides.

$17640000-15681600=E H^{2}+15681600-15681600$

$1958400=E H^{2}$

Taking square root on both sides, we get

$1399.428=EH$

$1400 \approx EH$

The distance from space station to the horizon is approximately 1400 miles.