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:
[tex](x+4000)^{2}= 4000^{2} + 210^{2} [/tex]
[tex](x+4000)^{2}=16000000+44100=16044100[/tex]
taking the square roots of both sides we get:
[tex]x+4000=+- \sqrt{16044100} =+-4005.5087[/tex]
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
