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24 August, 07:05

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.)

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  1. 24 August, 08:46
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    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
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