MATH SOLVE

3 months ago

Q:
# URGENT!!! Amy, on a jog, runs in a straight line for 3 miles. She then changes direction, heading 50 degrees to the right and runs for 6 miles in this direction. How far is Amy from her starting position? (Round your final answer to the nearest tenth place.) ANSWER THE QUESTION ONLY

Accepted Solution

A:

Answer:8.2500000000 milesStep-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} Β - 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.