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.)

how far is the ship from shore when the stack disappears from the sailor's view = 29.73 m

Step-by-step explanation:

you will see this makes a right triangle

the height is 6,400,000 m+4 m=6,400,004m

the hypotenuse is 6,400,000 m+30 m=6,400,030m

By Pythagorus theorem:

the distance of the ship D^2 = 6,400,030^2 - 6,400,004^2

= (6,400,030 - 6,400,004) x (6,400,030 + 6,400,004)

[because a^2-b^2 = (a-b) x (a+b) ]

=26x34

D^2=884 m

D = 29.73 m