# Math Help - homework question...pythag th i think

1. ## homework question...pythag th i think

Assume the earth is a perfectly round sphere with a radius of 4000 miles and that 1 mile=5280 feet. How far does the horizon appear to be to a 5-ft person on a clear day? Explain.

i thought the answer would be just a small fraction over 4000 miles, so essentially the height of the man does not change how far the horizon appears to the man.

am i on the right track here?

2. Originally Posted by igottaquestion
Assume the earth is a perfectly round sphere with a radius of 4000 miles and that 1 mile=5280 feet. How far does the horizon appear to be to a 5-ft person on a clear day? Explain.

i thought the answer would be just a small fraction over 4000 miles, so essentially the height of the man does not change how far the horizon appears to the man.

am i on the right track here?
You are dealing with a right triangle. (See attachment)

The distance from the eye of the observer to the horizon is calculated according to Pythagorean theorem:

$d^2+4000^2 = \left(4000+\frac5{5280}\right)^2$

Solve for d
Spoiler:
I've got $d \approx 2.75\ mi$. If you want to increase the radius of the field of observation you should climb a hill or use a lighthouse.