The summit of Mauna Kea is approximately 13,796 ft above sea level. What is the distance from the summit to the horizon, rounded to the nearest mile?

Question

Assume that the distance from the center of the earth to any point on the earth's surface is 4,000 miles.

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Answer 1 · 2018-06-05T16:54:01

About 145 miles.

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#r=4000#

#v=13796/5280# (divide by 5280 to convert to miles)

Using Pythagorean's Theorem:

#a^2+b^2=c^2#

#a^2+4000^2=(4000+13796/5280)^2#

#a^2=(4000+13796/5280)^2-4000^2#

#a=sqrt((4000+13796/5280)^2-4000^2)~~144.6#