posted by jen .
Please imagine a triangle here. >.< the 'o' is a person and the two peaks are the mountains.
Explain why the distance between these two peaks are greater than the difference of the distances from the person to each peak.
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.