Chapter 8.3, Problem 53AE

Soccer Angles A soccer goal is 8 yards wide. Suppose a goalie is standing on her line in the center of her goal as a striker from the opposing team moves the ball towards her. The near post angle, $\alpha$, is formed by rays extending from the ball to the near post and the goalie. Similarly, the far post angle, $\beta$, is formed by rays extending from the ball to the far post and the goalie. See the figure.

a. Determine the near post angle and the far post angle when the striker is 20 yards from the near post and 24 yards from the far post.

b. How far is the goalie from the ball?

c. To cover the near post, the goalie moves toward the near post in order to make the near post angle and the far post angle equal. How far toward her near post does the goalie need to move?