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.

Hint: The earth’s radius is about 3,960 miles, and there are 5,280 feet in a mile.

Answer: 9.5 miles

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.