Question

Use the fact that the radius of the earth is 3960 miles and 1 mile is 5280 feet to answer the following question. A tower of a submarine is approximately 20 feet above sea level. How far can a person see from the top of the tower?

Answer 1

Alright, lets get started.

Please refer the diagram I have attached.

The height of the tower is = 20 feet

Converting this height into miles =
`(20)/(5280)` 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 =
`0.00378 + 3960 = 3960.00378`

Side BC = 3960 miles

Using Pythagorean theorem,

`AC^2 = AB^2 + BC^2`

`3960.00378^2 = 3960^2 + AB^2`

`15681629.9376 = 15681600 + AB^2`

`AB^2 = 29.9376`

Taking square root in both sides

AB = 5.47 miles

So, the answer is 5.47 miles. : Answer

Hope it will help :)