Homework Help for Precalculus

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Precalculus deals with preparatory or introductory fundamental abilities and knowledge required to study Calculus.

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Lv1
in Precalculus·
9 Aug 2022
A soccer field has a rectangular penalty area that measures 138 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. 
 
Suppose a penalty kick is taken from a comer 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 = 57 feet and b = 55 feet.
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Now suppose the goalkeeper stands in the center. A penalty kick is taken from a corner of the penalty area at position A (see the figure below). The goalkeeper stands in the center of the goal and can thus block a shot anywhere along segment  CD. To score, the shooter must kick the ball within the angle CAE or angle DAF. Find the sum of these two angles to the nearest tenth of a degree. Assume a = 57 feet and b = 55 feet.

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Based on your answers to the questions above, should the goalkeeper stand to the side or at the center of the goal? Why?
⚪ The goalkeeper should stand to the side so that the shooter has a larger angle in which to make a scoring kick.
⚪ The goalkeeper should stand at the center so that the shooter has a smaller angle in which to make a scoring kick.
⚪ The goalkeeper should stand to the side so that the shooter has a smaller angle in which to make a scoring kick.
⚪ There is no advantage for the goalkeeper standing to the side or at the center.
⚪ The goalkeeper should stand at the center so that the shooter has a larger angle in which to make a scoring kick.

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