Coach Haverty is setting up a tetherball court on the school playground so that the ball can only swing out $60^\circ$ from the pole. As Coach Haverty looks from the school playground at the pole, there is a fence to the left of the pole and a sidewalk to the right of the pole. Coach Haverty wants to ensure that no one will get hurt while playing tetherball, so he wants the rope to only extend $5$ feet out from the pole as measured along the ground.

1. Draw a diagram of this situation.

   Answer (a):

   

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

   Step 1 (b):

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

   Step 2 (b):

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

   Answer (b):

   $x ≈ 5.8$ feet