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13. A soccer goal is 24 ft wide. Point A is 40 ft in front 40 B. of the center of the goal. Point B is 40 ft in front of the right goal post. a. Which angle is larger, LA or 4B? b. From which point would you have a better chance of kicking the ball into the goal? Why? 24

13. A soccer goal is 24 ft wide. Point A is 40 ft in front 40 B. of the center of the goal. Point B is 40 ft in front of the right goal post. a. Which angle is larger, LA or 4B? b. From which point would you have a better chance of kicking the ball into the goal? Why? 24

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**Understanding Angle Calculation in Soccer Kicks** **Problem 13:** A soccer goal is 24 feet wide. Point A is 40 feet in front of the center of the goal. Point B is 40 feet in front of the right goal post. **a.** Which angle is larger, ∠A or ∠B? **b.** From which point would you have a better chance of kicking the ball into the goal? Why? **Diagram Explanation:** The diagram associated with the problem shows a rectangular representation of a soccer goal and the positions of points A and B relative to this goal. The goal is 24 feet wide. Point A is situated 40 feet directly in front of the center of the goal. Point B is 40 feet in front of the right goal post. The diagram also outlines the angles ∠A and ∠B, which need to be compared. Triangle visualization is crucial here: - Triangle A includes the point A, the left and right goalposts, and the center line of the goal. - Triangle B includes point B and the left and right goalposts. To understand which angle is larger, you can use geometric techniques such as constructing auxiliary lines or using trigonometric methods (e.g., calculating tangents to find the measures of the angles). **Detailed Analysis:** - Observing the diagram, it’s clear that Point A is at the midpoint in front of the goal, thus equally favorable in terms of distance to either post. - Point B is closer to the right goalpost, creating a narrower angle towards the left post. ### Educational Insight: Understanding how angles work in soccer can help improve goal-shooting accuracy. The wider the angle, the better chance a player has to score, because the target space (goal width) appears larger. Thus, players should aim to position themselves where they maximize this angle to the goalposts. --- Calculating tangents or analyzing geometric relations here can significantly help students in understanding practical applications of mathematical concepts in sports.
Transcribed Image Text:**Understanding Angle Calculation in Soccer Kicks** **Problem 13:** A soccer goal is 24 feet wide. Point A is 40 feet in front of the center of the goal. Point B is 40 feet in front of the right goal post. **a.** Which angle is larger, ∠A or ∠B? **b.** From which point would you have a better chance of kicking the ball into the goal? Why? **Diagram Explanation:** The diagram associated with the problem shows a rectangular representation of a soccer goal and the positions of points A and B relative to this goal. The goal is 24 feet wide. Point A is situated 40 feet directly in front of the center of the goal. Point B is 40 feet in front of the right goal post. The diagram also outlines the angles ∠A and ∠B, which need to be compared. Triangle visualization is crucial here: - Triangle A includes the point A, the left and right goalposts, and the center line of the goal. - Triangle B includes point B and the left and right goalposts. To understand which angle is larger, you can use geometric techniques such as constructing auxiliary lines or using trigonometric methods (e.g., calculating tangents to find the measures of the angles). **Detailed Analysis:** - Observing the diagram, it’s clear that Point A is at the midpoint in front of the goal, thus equally favorable in terms of distance to either post. - Point B is closer to the right goalpost, creating a narrower angle towards the left post. ### Educational Insight: Understanding how angles work in soccer can help improve goal-shooting accuracy. The wider the angle, the better chance a player has to score, because the target space (goal width) appears larger. Thus, players should aim to position themselves where they maximize this angle to the goalposts. --- Calculating tangents or analyzing geometric relations here can significantly help students in understanding practical applications of mathematical concepts in sports.
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