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8th Edition

Charles P. McKeague + 1 other

Publisher: Cengage Learning

ISBN: 9781305652224

Chapter 2.3, Problem 59PS

Textbook Problem

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Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet by 54 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 his or her position for a total coverage of 12 feet. *(Source: FĂ©dĂ©ration Internationale de Football Association)*

A penalty kick is taken from a corner of the penalty area at position *A* (see Figure 12). 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.

Figure 12

To determine

**To find:**

Themeasure of the sum of the angles

**Given information:**

A rectangular soccer field with the penalty area measuring 132 feet by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. It is assumed that the goalkeeper can block a shot 6 feet to either side of his or her position for a total coverage of 12 feet.

Now a penalty kick is taken from a corner of the penalty area at position A (as shown in the above diagram). 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.

**Concept Used:**

**Calculation:**

Let’s assume;

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Round to...Ch. 2 - Use a calculator to find to the nearest tenth of...Ch. 2 - Use a calculator to find to the nearest tenth of...Ch. 2 - The following problems refer to right triangle ABC...Ch. 2 - The following problems refer to right triangle ABC...Ch. 2 - The following problems refer to right triangle ABC...Ch. 2 - The following problems refer to right triangle ABC...Ch. 2 - Geometry If the altitude of an isosceles triangle...Ch. 2 - Angle of Elevation If the angle of elevation of...Ch. 2 - Distance Two guy wires from the top of a 35-foot...Ch. 2 - Vector Angle Vector V has a horizontal vector...Ch. 2 - Velocity A bullet is fired into the air with an...Ch. 2 - Distance and Bearing A ship travels 120 miles on a...Ch. 2 - Force Tyler and his cousin Kelly have attached a...Ch. 2 - Force Tyler and Kelly decide to rollerskate. 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Essentials Of Statistics

(a) Find the intervals of increase or decrease. (b) Find the local maximum and minimum values. (c) Find the int...

Single Variable Calculus: Early Transcendentals, Volume I

Graph the following points and their opposites on the real number line: 1, -2, and 4.

Intermediate Algebra

Simplify the expressions in Exercises 97106. 41/147/2

Applied Calculus

Circles and Lines Find equations for the circle and the line in the figure. 147.

Precalculus: Mathematics for Calculus (Standalone Book)

Define the terms statistic and parameter and explain how these terms are related to the concept of sampling err...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the expression sin Exercises 116. 23

Finite Mathematics and Applied Calculus (MindTap Course List)

Stephens, Atkins, and Kingston (2009) conducted a research study demonstrating that swearing can help reduce pa...

Statistics for The Behavioral Sciences (MindTap Course List)

Proof Prove that if f(x) 0. limxaf(x) = 0, and limxag(x) = then limxaf(x)g(x)=.

Calculus: Early Transcendental Functions (MindTap Course List)

Oil Leak At 1:00 p.m., oil begins leaking from a tank at a rate of (4+0.75t) gallons per hour. (a) How much oil...

Calculus of a Single Variable

Assuming that the exact area of a sector determined by a 400 arc is 94 cm2, find the length of the radius of th...

Elementary Geometry for College Students

PRODUCTION SCHEDULING Acoustical Company manufactures a DVD storage cabinet that can be bought fully assembled ...

Finite Mathematics for the Managerial, Life, and Social Sciences

Nielsen Media Research identified Empire and the Big Bang theory as the two top-rated prime-time television ser...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The estimated regression equation for a model involving two independent variables and 10 observations follows. ...

Statistics for Business & Economics, Revised (MindTap Course List)

Find the decimal value of each of the distances A, B, C, D, and E in Figure 96. Note the total unit value of th...

Mathematics For Machine Technology

Using the Definition of Limit In Exercises 45-56, find the limit L. Then use the definition to prove that the...

Calculus (MindTap Course List)

Suppose that you wake up in the morning with all the symptoms of a head cold. You take a cold pill and eat a bi...

Research Methods for the Behavioral Sciences (MindTap Course List)

True or False:
converges.

Study Guide for Stewart's Multivariable Calculus, 8th

Cylindrical-to-Rectangular ConversionIn Exercises 2330, find an equation in rectangular coordinates for the sur...

Multivariable Calculus

Give brief definitions of the terms descriptive statistics and inferential statistics.

Introduction To Statistics And Data Analysis

Under what circumstances are the median and the mode considered to be better than the mean for describing centr...

Research Methods for the Behavioral Sciences (MindTap Course List)

Discovery and Writing Does 0.999 = 1? Explain.

College Algebra (MindTap Course List)

The quadratic approximation for at a = 1 is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In Exercises 1-6, find the periodic rate that corresponds to the given compound rate, if the rate is compounded...

Mathematics: A Practical Odyssey

An urn contains five balls numbered 1,2,2,8, and 8. If a person selects a set of three balls at random, what is...

Discrete Mathematics With Applications

In Problems 3–12 use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value....

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

10. The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an inf...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Cost of Residential Water. On its municipal website, the city of Tulsa states that the rate it charges per 5 CC...

Essentials Of Statistics For Business & Economics

TEST YOUR UNDERSTANDINGFOR EXAMPLE 5.15 What range of lumber volume is available for a 10-foot-long log? EXAMPL...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

For the following exercises, find the domain, range, and all zeros/intercepts, if any, of the functions. 17. f(...

Calculus Volume 1

Performing Operations In Exercises 23-30, perform the operation(s). (Write fractional answers in simplest form....

College Algebra