Tonight, as I drove along the long stretch of road from Longview to Dallas, Texas, I couldn’t help but wonder how far away the horizon is.
Now, I’m not completely math illiterate, so I decided to figure it out. The problem is… My answer doesn’t seem right. Perhaps I have done something wrong. See if any of you find a mistake in my method:
The Earth is perfectly round
Our test subject is 5.8 feet tall.
Because the Earth is so big, the distance ‘x’ (shown below) is a close enough approximation of the arc length and actual driving distance to the horizon.
Okay! Calculation time!
According to Wikipedia, the radius of the earth is an average of about 3956.545 miles * 5280 ft/mile=
Add 5.8 feet to that and we get a hypotenuse of 20890563.4 ft
according to Pythagoras
20890557.6^2 + x^2 = 20890563.4^2
so x^2 = 24330501.8
x is about equal to 15566.96 ft
Divide by 5280 and we get… 2.948 miles. That’s so… short… did I do something wrong?