Answer:
8.2500000000 miles
Explanation:
I drew a triangle to illustrate the reference triangle.
So, Amy ran from summit A for 3 miles then turned to her right by 50 degrees (creating angle B of 130 degrees), and runs for another 6 miles.
Based on the Cosines Law, we have:

If we isolate b, we have the following formula.

So, as she stops at summit C, she's 8.25 miles away from her starting point.