Hello, strummer!

A sailor at the seashore watches a ship with a smokestack 30 meters above water level

as the ship steams out to sea. . The sailor's eye level is 4 meters above water level.

About how far is the ship from shore when the stack disappears from the sailor's view?

(The radius of Earth is about 6400 kilometers.) Code:

A C B
o - - - - * o * - - - - o
4\ * | * /30
* | *
* \ |R / *
R \ | / R
* \ | / *
* o *
* O *
* *
* *
* *
* * *

The sailor is at , the top of the smokestack is

The line of sight is tangent to the Earth at

The center of Earth is , its radius is (6,400,000 m).

In right triangle

In right triangle

Hence: .

. . . . . . . . .

. . . . . . . . . m.

Therefore, the distance is about 26.75 kilometers.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Edit . . .

Ah, I see that skeeter did it *correctly* (ship-to-shore distance).

Using the Law of Cosines, is given by:

. .

Hence: . radians.

Therefore: . km