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8th Edition

Charles P. McKeague + 1 other

Publisher: Cengage Learning

ISBN: 9781305652224

Chapter 2.3, Problem 58PS

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 11). 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.

Figure 11

To determine

**To find:**

Themeasure of the angle

**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 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).

**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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In Exercises 17 to 24, let U = {2. 6, 8, 10, 12, 14, 16, 18}, A = {2, 6, 10}, B = {6, 10, 16, 18}, and C = {14,...

Mathematical Excursions (MindTap Course List)

Market Research A market analyst working for a small-appliance manufacturer finds that if the firm produces and...

Precalculus: Mathematics for Calculus (Standalone Book)

Exercises You can use the following problems as a self-test on the material presented in this review. If you ca...

Essentials Of Statistics

Evaluate the indefinite integral. cos(t/2)dt

Calculus: Early Transcendentals

a. In a Poisson process, what has to happen in both the time interval (0, t) and the interval (t, t + t) so tha...

Probability and Statistics for Engineering and the Sciences

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Identify the independent and dependent variables for each equation: v=506t

Elementary Technical Mathematics

For the following scores, the smallest value is X 7 and the largest value is X 48. a. Determine the best inte...

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

Finding an Indefinite Integral In Exercises 1738, use integration tables to find the indefinite integral. arcsi...

Calculus: Early Transcendental Functions (MindTap Course List)

Lateral Surface Area of a Cone A right circular cone is generated by revolving the region bounded by y=3x/4,y=3...

Calculus of a Single Variable

In Exercises 39 to 42, use substitution to solve the system. Use Example 9 as a guide. x=d and y=fx+g.

Elementary Geometry for College Students

In Exercise 5761, determine whether the statement is true or false. If it is true, explain why it is true. If i...

Finite Mathematics for the Managerial, Life, and Social Sciences

In terms of mathematical models, what is the basic difference between exponential growth and exponential decay?

Mathematics: A Practical Odyssey

For y = 3x + tan x, y = _____. a) 3 + sec x b) 3x sec2 x + 3 tan x c) 3 + sec2 x d) x cos x + sin x

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

Evaluating a Line Integral in Differential Form In Exercises 5764, evaluate C(2xy)dx+(x+3y)dy. C: line segments...

Multivariable Calculus

) Ideas for future research studies often can be obtained from the discussion sections of research reports. Occ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Solve each of the following equations using the addition principle of equality. Check each answer. 25=d9

Mathematics For Machine Technology

In this chapter, we introduced the observational research design, the survey research design, and the case stud...

Research Methods for the Behavioral Sciences (MindTap Course List)

The Troubled Asset Relief Program (TARP), passed by the U.S. Congress in October 2008,provided 700 billion in a...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Finding Tangent Lines There are two tangent lines from the point (0, 1) to the circle x2 + (y + l)2 = 1 (see fi...

Calculus (MindTap Course List)

Use a graphing calculator to graph each equation and then find the x-coordinate of the x-intercept to the neare...

College Algebra (MindTap Course List)

The figure at the right shows one point P on a conic and the distances of P to the focus and the directrix of a...

Study Guide for Stewart's Multivariable Calculus, 8th

In a regression analysis involving 30 observations, the following estimated regression equation was obtained: ...

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

Based on observing more than 400 drivers in the Atlanta area, two investigators at Georgia State University con...

Introduction To Statistics And Data Analysis

Reaction Rates In a chemical reaction, the reaction rate R is a function of the concentraton of the product of ...

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

In Problems 710, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order DE x + x = ...

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

Beer and Cider Consumption. According to the National Beer Wholesalers Association, U.S. consumers 21 years and...

Essentials Of Statistics For Business & Economics

Differences in Insurance Claims Based on Marital Status. A large automobile insurance company selected samples ...

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

Use the unique factorization theorem to write the following integers in standard factored form. 1,176 5,733 3,6...

Discrete Mathematics With Applications

[T] In physics, the magnitude of an electric field generated by a point charge at a distance r in vacuum is gov...

Calculus Volume 1

Determining the Equation of a Graph Determine whether the graph represents equation (a), (b), or (c). Explain y...

College Algebra