Bob is hanging a swing so that it can swing a total angle of $120^\circ$. 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 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?

   Step 1 (b):

   $\cos30^{\circ}=\frac{5}{x}$ 

   Step 2 (b):

   $x=\frac{5}{\cos 30^{\circ}}$