SOLUTION: From the top of Mt Washington, which is 6288 feet above sea level, how far is it to the horizon? Assume that the earth has a 3962 mile radius and give your answer to the nearest

Question 149250: From the top of Mt Washington, which is 6288 feet above sea level, how far is it to the horizon? Assume that the earth has a 3962 mile radius and give your answer to the nearest mile.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
First, find the height of Mt. Washington above sea level
in miles.
(6288 ft)(1 mi / 5280 ft) = 1.191 mi
At the horizon, the radius of the earth forms a right angle with
a sight line from the top of the mountain because the sight line
would be tangent to the surface
Now find the length of the earth's radius plus the height of
Mt Washington
1.191 + 3962 = 3963.19 mi
Now find the angle whose cosine is 3962 / 3963.19 = .9996995
On my calculator, I get 1.4046409 degrees
Now find the tangent of this angle since
tangent angle = distance to horizon / radius of earth
tan(1.4046409) = .02452052
distance to horizon = .02452052 x 3962
distance to horizon = 97.15 mi
To the nearest mile the distance to the horizon is 97 mi
I checked this using the pythagorean theorem

This checked out very close
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