math help needed?

Draw a line from the center of the Earth to the top of the person.
Draw a line from the center of the Earth to the horizon point.
Draw a perpendicular line from the horizon to the person.

You have created a right triangle.

The distance to the horizon is one leg of this triangle, call that distance x.
The other leg is the radius of the earth. (3959)
The hypotenuse is the height of the person above the center of the earth. (3959 + 0.398 = 3959.398)

Use the Pythagorean Theorem:
x² + 3959² = 3959.398²
x² = 3959.398² - 3959²
x² ≈ 3151.522404

Take the square root (we only care about the principal, positive square root because this is a distance):
x ≈ √3151.522404
x ≈ 56.13842182

Round to the nearest mile.

Answer:
About 56 miles

d^2 + r^2 = (r + h)^2
Assuming the Earth's surface is perfectly spherical (which it's not):
d^2 + 3959^2 = (3959 + 0.398)^2
d^2 + 15673681 = 3959.398^2
d^2 + 15673681 = 15676832.522404
d^2 = 15676832.522404 - 15673681
d^2 = 3151.522404
d = sqrt(3151.522404), note that d can't be negative
d =~ 56.138421816078869888549930193327 miles

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