Distance to the Horizon
Puzzle:
You’re on a cruise ship in the middle of the ocean and
wonder how far you can see. You estimate that you’re
about 60 feet above sea level.
Show Hint
Hint: The earth’s
radius is about 3,960 miles, and there are 5,280
feet in a mile.
Show Answer
Show Solution
Solution:
Your line of sight to the horizon is tangent to
the earth. This creates a right triangle with
the horizon at one point (the right angle), the center
of the earth at the second point, and you at the third.
The hypoteneuse is the edge between you and the
center. That edge is the radius of the earth plus
60 feet. The edge between the right angle and the
center is just the radius. Use the Pythagorean theorem
to find the third edge, which is 9.5 miles.
If you’re standing on the beach, your height
is about 6 feet, which makes the distance to
the horizon almost exactly 3 miles.
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