The summit of Mount 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

About 145 miles.

Explanation:

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

Step-by-step explanation:

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  =  √(4000  +  13796   /5280)^2  −  4000^2  ≈  144.6

This is just a shrunk down version so it is easier to read. All credit goes to the other answer.

it has the same slope and a different y-intercept

hope this : )