Question

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

Answer 1

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:

`cos(B) = (c^(2) + a^(2)  - b^(2) )/(2 * c * a)`

If we isolate b, we have the following formula.

`b = \sqrt{a^(2) + c^(2) - 2 * a * c * cos(B) } \\ \\b = \sqrt{6^(2) + 3^(2) - 2 * 6 * 3 * cos(130) } = 8.25`

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