Posted by jen on Monday, November 15, 2010 at 2:45am.
Please imagine a triangle here. >.< the 'o' is a person and the two peaks are the mountains.
/\___/\
_\___/
___o
Explain why the distance between these two peaks are greater than the difference of the distances from the person to each peak.

Geometry  MathMate, Monday, November 15, 2010 at 9:04am
In any nondegenerate 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>ACBC, which translates to the distance between the two mountains is greater than the difference between the distances from the person to the mountains.

Geometry  jen, Tuesday, November 16, 2010 at 4:34am
Thanks MathMate.
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