Answer:
The pilot's distance to the horizon is 267.2 kilometers.
Step-by-step explanation:
According to the below diagram, [tex]A[/tex] is the position of the pilot which is 5.6 kilometers above the earth's surface, [tex]D[/tex].
Earth has a radius of 6371 kilometers. That means, [tex]CB=CD= 6371[/tex] kilometers.
So, [tex]CA= CD+DA= (6371+5.6)= 6376.6[/tex] kilometers.
The pilot's distance to the horizon is [tex]AB[/tex].
Using Pythagorean theorem, we will get........
[tex]AB^2+CB^2 = CA^2\\ \\ AB^2+(6371)^2=(6376.6)^2\\ \\ AB^2 = (6376.6)^2 -(6371)^2 \\ \\ AB^2= 71386.56\\ \\ AB= \sqrt{71386.56}=267.182... \approx 267.2[/tex]
(Rounded to the nearest tenth)
So, the pilot's distance to the horizon is 267.2 kilometers.
