Farmer Jill has a problem. She lives on a triangular plot of land that is surrounded on all three sides by a fence. Yesterday, one side of the fence was torn down in a storm. She wants to determine the length of the side that needs to be rebuilt so she can purchase enough lumber. Since the weather is still too poor for her to go outside and measure the distance, she decides to use the lengths of the two sides that are still standing ($116$ feet and $224$ feet) and the angle between them $(58^\circ)$.  

1. Draw a diagram of this situation. Label all of the sides and angles that Farmer Jill has measurements for.

   Answer (a):

   

2. Find the length of the fence that needs to be replaced. Show all work. Which tool did you use?

   Hint (b):

   Use the Law of Cosines, $c^2=a^2+b^2-2ab\cos C$. The angle that you know $(58º)$ has to correspond to $∠C$, so that you can calculate $\cos C$.