A soccer field has a rectangular penalty area that measures 128 feet by 55 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of their position for a total coverage of 12 feet. A penalty kick is taken from a corner of the penalty area at position A (see the figure below). The goalkeeper stands 6 feet from the goalpost nearest the shooter and can thus block a shot anywhere between the middle of the goal and the nearest goalpost (segment CD). To score, the shooter must kick the ball within the angle CAE. Find the measure of this angle to the nearest tenth of a degree. Assume a = 52 feet and b = 55 feet

A soccer field has a rectangular penalty area that measures 128 feet by 55 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of their position for a total coverage of 12 feet.

A penalty kick is taken from a corner of the penalty area at position A (see the figure below). The goalkeeper stands 6 feet from the goalpost nearest the shooter and can thus block a shot anywhere between the middle of the goal and the nearest goalpost (segment CD). To score, the shooter must kick the ball within the angle CAE. Find the measure of this angle to the nearest tenth of a degree. Assume a = 52 feet and b = 55 feet