Question 18886
Draw a picture of a right triangle where one short side is the unknown distance D, and the other is the radius of earth, R . The long side is the radius of earth plus the height of the mountain, R+H where R=3963 miles and H=13,677 feet. Of course we need to use consistent units, and so we convert the height of the mountain to {{{h=(13677)/(5280)}}}  miles. The Pythagorean Theorem tell us that  {{{(R^2)+(D^2)=(R+H)^2}}}

We need to know D. Expanding on the right and subtracting {{{R^2}}} on both sides gives the equation {{{D^2=R^2+2RH+H^2-R^2=RH+H^2}}}

Other wise as {{{D=sqrt(2RH+H^2)}}}


Plugging in the values we are given yields D=143.31 miles