Answer:
8.2500000000 miles
Step-by-step 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:
[tex]cos(B) = \frac{c^{2} + a^{2} - b^{2} }{2 * c * a}[/tex]
If we isolate b, we have the following formula.
[tex]b = \sqrt{a^{2} + c^{2} - 2 * a * c * cos(B) } \\ \\b = \sqrt{6^{2} + 3^{2} - 2 * 6 * 3 * cos(130) } = 8.25[/tex]
So, as she stops at summit C, she's 8.25 miles away from her starting point.
