I hope this is the right area to ask to this question

I was just wondering if it were possible to triangulate a distance supposedly unknown. Let's say we know it's 258 miles from Vegas to San Diego and we know it's 256 miles from Vegas to Phoenix but we want to find out the distance between Phoenix and San Diego. Is there a way to find this mathematically or do we have missing info? (I do know the distance, I am just wondering if you could figure it out without looking it up)

Drew it and linked to it here on Google Maps

https://maps.google.com/maps/ms?msid=203963142651048612558.0004e3a4f9efa1676a5f 9&msa=0&ll=34.343436,-114.125977&spn=5.232766,10.821533

There is not information given to find the length of the side. You need to know the angles created by your drawing. Once the angles are know then you can work out such things as missing angles and missing length of sides, as per your diagram. E.g. sine rule.

How do I measure the angles?

You need to know just one angle - then you could use law of sines and/or cosines to find the unknown angles and lengths. You can find the angles if you know the bearings from Vegas to SD and from Vegas to Phoenix - does Google Maps provide that info for you?

This method assumes the world is flat, so there will be some error introduced as it ignores the earth's curvature.

With a right triangle...

a^2 + b^2 = c^2
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Of course I can not visualize the map here so I do not know if a right triangle is possible.