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8th Edition

Charles P. McKeague + 1 other

Publisher: Cengage Learning

ISBN: 9781305652224

Chapter 2.3, Problem 60PS

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 the center of the penalty area at position *A* (see Figure 13). 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 13

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 G be the mid-point of CD and CG = GD = 6ft;

Trigonometry (MindTap Course List)

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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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Calculus (MindTap Course List)

Explain why each function is continuous or discontinuous. (a) The temperature at a specific location as a funct...

Single Variable Calculus

30. The figure shows a graph of the future value of $350 at 6% compounded monthly, along with the graph of $350...

Mathematical Applications for the Management, Life, and Social Sciences

Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point...

Calculus: An Applied Approach (MindTap Course List)

Given n(J) = 245, n(K) = 178, and n(J âˆª K) 310, find n(J âˆ© K).

Mathematical Excursions (MindTap Course List)

In Exercises 1- 9, let G be the given group. Write out the elements of a group of permutations that is isomorph...

Elements Of Modern Algebra

Finding an Indefinite Integral In Exercises 19-32, find the indefinite integral. xarcsinxdx

Calculus of a Single Variable

Use drawings, as needed, to answer each question. Suppose that rs. Both interior angles 4 and 6 have been bisec...

Elementary Geometry for College Students

Sketching a Polar Graph In Exercises 87-96, sketch a graph or the polar equation. r=4

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 45-48, determine whether the statement is true or false. If it is true, explain why it is true. If...

Finite Mathematics for the Managerial, Life, and Social Sciences

Two shipping services offer overnight delivery of parcels, and both promise delivery before 10 A.M. A mail-orde...

Introduction To Statistics And Data Analysis

Explain why we can be more confident about causal relationships between variables when a quasi-experimental des...

Research Methods for the Behavioral Sciences (MindTap Course List)

Power Series Solution In Exercises 59 and 60, use a power series to solve the differential equation. y+3xy3y=0

Multivariable Calculus

log27 9 =

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

To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each c...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain the role of voluntary participation in informed consent.

Research Methods for the Behavioral Sciences (MindTap Course List)

In Exercises 2142, Define the necessary symbols, rewrite the argument in symbolic form, and use a truth table t...

Mathematics: A Practical Odyssey

Which function best fits the graph at the right?
a) f(x, y) = 4 – x2
b) f(x, y) = 4 – y2
c) f(x, y) = 4 – xy
d...

Study Guide for Stewart's Multivariable Calculus, 8th

Solve each absolute value equation for x. |4x2x|=3

College Algebra (MindTap Course List)

Forty-three percent of Americans use social media and other websites to voice their opinions about television p...

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

Center of Mass of a Planar Lamina In Exercises 15-28, find Mx,My , and (x, y) for the lamina of uniform density...

Calculus (MindTap Course List)

Use Figure 9-4 to answer Exercises 16. All dimensions are in inches. 2. Distance B=_

Mathematics For Machine Technology

Meticulous Drill Reamer (MDR) specializes in drilling and boring precise holes in hard metals (e.g., steel all...

Essentials Of Statistics For Business & Economics

15. The National Football League (NFL) polls fans to develop a rating for each football game (NFL website, Octo...

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

In Problems 41–46 use Theorem B.3 to find A–1 for the given matrix or show that no inverse exists.
42.

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

Getting a Formula In Exercises S-4 through S-13, a verbal description of a function is given. Use a formula to ...

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

Given a function f:RR , to prove that f is decreasing, you suppose that and then you show that _____.

Discrete Mathematics With Applications

Forming a Committee A local college is forming a six-member research committee with one administrator, three fa...

College Algebra

In the following exercises, find each indefinite integral by using appropriate substitutions. 334. In( sinx)tan...

Calculus Volume 2