Please imagine a triangle here. >.< the 'o' is a person and the two peaks are the mountains.

Question

/\___/\
_\___/
___o
Explain why the distance between these two peaks are greater than the difference of the distances from the person to each peak.

Answer 1

In any non-degenerate triangle, the sum of any two sides is always greater than the third side.

Let A,B represent the two peaks, and C the person.

From the first statement, we can conclude that AB+BC>AC, or equivalently AB>AC-BC, which translates to the distance between the two mountains is greater than the difference between the distances from the person to the mountains.

Answer 2

Thanks MathMate.