Alright, lets get started.
Please refer the diagram I have attached.
The height of the tower is = 20 feet
Converting this height into miles = [tex] \frac{20}{5280} [/tex] miles
So, height of the tower = 0.00378 miles
Say the top of the tower is point A, and the farthest distance can be seen here is point B.
It will form a right angle triangle. Say the centre of earth is C, then
Side AC will be = tower + radius
AC = [tex] 0.00378 + 3960 = 3960.00378 [/tex]
Side BC = 3960 miles
Using Pythagorean theorem,
[tex] AC^2 = AB^2 + BC^2 [/tex]
[tex] 3960.00378^2 = 3960^2 + AB^2 [/tex]
[tex] 15681629.9376 = 15681600 + AB^2 [/tex]
[tex] AB^2 = 29.9376 [/tex]
Taking square root in both sides
AB = 5.47 miles
So, the answer is 5.47 miles. : Answer
Hope it will help :)
