Question

A mountain climber is standing at the top of Mount Everest. The distance from the summit to the horizon is 210 miles. About how high is Mount Everest?

Answer 1

Let DE, the height of mount Everest be x.

The center of the earth (point C), the horizont vanishing point (point H) and the top of mount Everest (point E) form a right triangle, where:
 
the hypothenuse is |EC|=|ED|+|DC|=x+4000              (DC is a radius)
|HC|=4000 mi
|HE|=210 mi

by the Pythagorean theorem:

 $(x+4000)^{2}= 4000^{2} + 210^{2}$

$(x+4000)^{2}=16000000+44100=16044100$

taking the square roots of both sides we get:

$x+4000=+- \sqrt{16044100} =+-4005.5087$

so x=-4000+4005.5087  miles = 5.5087  miles   
or x= -4000-4005.5  which is negative so not a solution to our problem



Answer: 5.5087  miles