Bob is hanging a swing from a pole high off the ground so that it can swing a total angle of $120º$. Since there is a bush $5$ feet in front of the swing and a shed $5$ feet behind the swing, Bob wants to ensure that no one will get hurt when they are swinging. What is the maximum length of chain that Bob can use for the swing?  

1. Draw a diagram of this situation.

   Answer (a):

   

2. What is the maximum length of chain that Bob can use? State what tools you used to solve this problem.

   Step 1(b):

   $\text{cos}30º = \frac{ 5 }{x}$

   Step 2(b):

   $x = \frac{ 5 }{\text{cos}30º}$

   Answer (b):

   $x\approx5.77$ feet