MR. MILLIGAN MATH 8 THIS BK BELNGS T CHAPTER 3 Real Numbers and the Pythagorean Theorem
ASSIGNMENT PAGE Date Assignment/ Homework Behavior Home Work Complete utstanding Assignments Signature
3 NAME DATE PERID Student-Built Glossary This is an alphabetical list of new vocabulary terms you will learn in Chapter 3. As you study the chapter, complete each term s definition or description. Remember to add the page number where you found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term Found on Page Definition/Description/Eample Chapter Resources abscissa [ab-sih-suh] converse coordinate plane hypotenuse irrational number legs ordered pair ordinate [R-din-it] origin Chapter 3 1 Course 3
3 Student-Built Glossary (continued) Vocabulary Term perfect square Found on Page Definition/Description/Eample Pythagorean Theorem quadrants radical sign real number square root -ais -coordinate y-ais y-coordinate Chapter 3 2 Course 3
3-1 Study Guide and Intervention Square Roots The square root of a number is one of two equal factors. The radical sign 2 is used to indicate a square root. Eamples Find each square root. 1 Since 1 1 1, 1 1. 16 Since 4 4 16, 16 4. 0.25 Since 0.5 0.5 0.25, 0.25 0.5. 2 5 3 6 Since 5 6 5 6 2 5, 36 2 5 3 6 5 6. Eample 5 Solve a 2 4 9. a 2 4 9 a 2 4 9 Write the equation. Take the square root of each side. a 2 3 or 2 3 Notice that 2 3 2 3 4 9 and 2 3 2 3 4 9. The equation has two solutions, 2 3 and 2 3. Eercises Find each square root. 1. 4 2. 9 3. 49 4. 25 5. 0.01 7. 9 16 6. 0.64 8. 2 ALGEBRA Solve each equation. 1 5 9. 2 121 10. a 2 3,600 11. p 2 81 12. t 1 00 2 1 2 1 196 Chapter 3 10 Course 3
3-1 Skills Practice Square Roots Find each square root. 1. 16 2. 9 3. 36 4. 196 5. 121 7. 0.04 6. 81 8. 289 Lesson 3 1 9. 0.81 10. 400 11. 1 6 49 12. 1 49 0 0 ALGEBRA Solve each equation. 13. s 2 81 14. t 2 36 15. 2 49 16. 256 z 2 17. 900 y 2 18. 1,024 h 2 19. c 2 4 9 20. a 64 2 25 1 21 1 21. 1 00 d2 22. 1 44 r 169 2 23. b 2 9 4 41 24. 2 1 2 1 400 Chapter 3 11 Course 3
3-1 Practice Square Roots Find each square root. 1. 3 6 2. 1 4 4 3. 9 1 6 121 5. 2.2 5 6. 7. 81 289 1 0 0 9. 0.4 9 10. 3.2 4 11. 25 4 4 1 4. 1.9 6 8. 0.0 0 2 5 12. 3 6 1 ALGEBRA Solve each equation. Check your solution(s). 13. h 2 121 14. 324 a 2 15. 2 81 1 69 16. 0.0196 m 2 17. y 6 18. z 8.4 19. GARDENING Moesha has 196 pepper plants that she wants to plant in square formation. How many pepper plants should she plant in each row? 20. RESTAURANTS A new restaurant has ordered 64 tables for its outdoor patio. If the manager arranges the tables in a square formation, how many will be in each row? GEMETRY The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each square. 21. 22. 23. Area 144 square inches Area 81 square feet Area 324 square meters Chapter 3 12 Course 3
3-1 Word Problem Practice Square Roots 1. PLANNING Rosy wants a large picture window put in the living room of her new house. The window is to be square with an area of 49 square feet. How long should each side of the window be? 2. GEMETRY If the area of a square is 1 square meter, how many centimeters long is each side? 3. ART A miniature portrait of George Washington is square and has an area of 169 square centimeters. How long is each side of the portrait? 4. BAKING Len is baking a square cake for his friend s wedding. When served to the guests, the cake will be cut into square pieces 1 inch on a side. The cake should be large enough so that each of the 121 guests gets one piece. How long should each side of the cake be? Lesson 3 1 5. ART Cara has 196 marbles that she is using to make a square formation. How many marbles should be in each row? 7. HME IMPRVEMENT Al has 324 square paving stones that he plans to use to construct a square patio. How many paving stones wide will the patio be? 6. GARDENING Tate is planning to put a square garden with an area of 289 square feet in his back yard. What will be the length of each side of the garden? 8. GEMETRY If the area of a square is 529 square inches, what is the length of a side of the square? Chapter 3 13 Course 3
3-2 Study Guide and Intervention Estimating Square Roots Most numbers are not perfect squares. You can estimate square roots for these numbers. Eample 1 Estimate 204 to the nearest whole number. The first perfect square less than 204 is 14. The first perfect square greater than 204 is 15. 196 204 225 Write an inequality. 14 2 204 15 2 196 14 2 and 225 15 2 14 204 15 Take the square root of each number. So, 204 is between 14 and 15. Since 204 is closer to 196 than 225, the best whole number estimate for 204 is 14. Eample 2 Estimate 79.3 to the nearest whole number. The first perfect square less than 79.3 is 64. The first perfect square greater than 79.3 is 81. 64 79.3 81 Write an inequality. 8 2 79.3 9 2 64 8 2 and 81 9 2 8 79.3 9 Take the square root of each number. So, 79.3 is between 8 and 9. Since 79.3 is closer to 81 than 64, the best whole number estimate for 79.3 is 9. Eercises Estimate to the nearest whole number. 1. 8 2. 37 3. 14 4. 26 5. 62 6. 48 7. 103 8. 141 9. 14.3 Lesson 3 2 10. 51.2 11. 82.7 12. 175.2 Chapter 3 17 Course 3
3-2 Skills Practice Estimating Square Roots Estimate to the nearest whole number. 1. 5 2. 18 3. 10 4. 34 5. 53 6. 80 7. 69 8. 99 9. 120 10. 77 11. 171 12. 230 13. 147 14. 194 15. 290 16. 440 19. 1,010 22. 17.8 25. 23.8 17. 578 20. 1,230 23. 11.5 26. 59.4 18. 730 21. 8.42 24. 37.7 27. 97.3 28. 118.4 29. 84.35 30. 45.92 Chapter 3 18 Course 3
3-2 Practice Estimating Square Roots Estimate to the nearest whole number. 1. 3 8 2. 5 3 3. 9 9 4. 2 2 7 5. 8.5 6. 3 5.1 7. 6 7.3 8. 1 0 3.6 9. 8 6.4 10. 4 5.2 11. 7 2 5 12. 2 7 3 8 rder from least to greatest. 13. 8, 10, 6 1, 7 3 14. 4 5, 9, 6, 6 3 15. 5 0, 7, 4 4, 5 Lesson 3 2 ALGEBRA Estimate the solution of each equation to the nearest integer. 16. d 2 61 17. z 2 85 18. r 2 3.7 19. GEMETRY The radius of a cylinder with volume V and height 10 centimeters is approimately V. If a can that is 10 centimeters tall has a volume of 900 cubic 30 centimeters, estimate its radius. 20. TRAVEL The formula s 1 8 d can be used to find the speed s of a car in miles per hour when the car needs d feet to come to a complete stop after slamming on the brakes. If it took a car 12 feet to come to a complete stop after slamming on the brakes, estimate the speed of the car. GEMETRY The formula for the area of a square is A s 2, where s is the length of a side. Estimate the length of a side for each square. 21. 22. Area 40 square inches Area 97 square feet Chapter 3 19 Course 3
3-2 Word Problem Practice Estimating Square Roots 1. GEMETRY If the area of a square is 29 square inches, estimate the length of each side of the square to the nearest whole number. 2. DECRATING Miki has an square rug in her living room that has an area of 19 square yards. Estimate the length of a side of the rug to the nearest whole number. 3. GARDENING Ruby is planning to put a square garden with an area of 200 square feet in her back yard. Estimate the length of each side of the garden to the nearest whole number. 4. ALGEBRA Estimate the solution of c 2 40 to the nearest integer. 5. ALGEBRA Estimate the solution of 2 138.2 to the nearest integer. 7. GEMETRY The radius r of a certain circle is given by r 71. Estimate the radius of the circle to the nearest foot. 6. ARITHMETIC The geometric mean of two numbers a and b can be found by evaluating a. b Estimate the geometric mean of 5 and 10 to the nearest whole number. 8. GEMETRY In a triangle whose base and height are equal, the base b is given by the formula b 2A, where A is the area of the triangle. Estimate to the nearest whole number the base of this triangle if the area is 17 square meters. Chapter 3 20 Course 3
3-3 Study Guide and Intervention Problem-Solving Investigation: Use a Venn Diagram You may need to use a Venn diagram to solve some problems. Understand Determine what information is given in the problem and what you need to find. Plan Select a strategy including a possible estimate. Solve Solve the problem by carrying out your plan. Check Eamine your answer to see if it seems reasonable. Eample f the 25 skiers on the ski team, 13 signed up to race in the Slalom race, and 8 signed up for the Giant Slalom race. Si skiers signed up to ski in both the Slalom and the Giant Slalom races. How many skiers did not sign up for any races? Understand Plan You know how many skiers signed up for each race and how many signed up for both races. You need to organize the information. You can use a Venn diagram to organize the information. Solve Draw two overlapping circles to represent the two different races. Place a 6 in the section that is a part of both circles. Use subtraction to determine the number for each other section. Check Eercise only the Slalom race: 13 6 7 only the Giant Slalom race: 8 6 2 neither the Slalom or the Giant Slalom race: 25 7 2 6 10 There were 10 skiers who did not sign up for either race. Check each circle to see if the appropriate number of students is represented. Use a Venn diagram to solve the problem. SPRTS The athletic club took a survey to find out what sports students might participate in net fall. f the 80 students surveyed, 42 wanted to play football, 37 wanted to play soccer, and 15 wanted to play both football and soccer. How many students did not want to play either sport in the fall? Ski Races 10 Slalom 7 6 Giant Slalom 2 Lesson 3 3 Chapter 3 23 Course 3
3-3 NAME DATE PERID Skills Practice Problem-Solving Investigation: Use a Venn Diagram Use a Venn diagram to solve each problem. 1. PHNE SERVICE f the 5,750 residents of Homer, Alaska, 2,330 pay for landline phone service and 4,180 pay for cell phone service. ne thousand seven hundred fifty pay for both landline and cell phone service. How many residents of Homer do not pay for any type of phone service? 2. BILGY f the 2,890 ducks living in a particular wetland area, scientists find that 1,260 have deformed beaks, while 1,320 have deformed feet. Si hundred ninety of the birds have both deformed feet and beaks. How many of the ducks living in the wetland area have no deformities? 3. FLU SYMPTMS The local health agency treated 890 people during the flu season. Three hundred fifty of the patients had flu symptoms, 530 had cold symptoms, and 140 had both cold and flu symptoms. How many of the patients treated by the health agency had no cold or flu symptoms? 4. HLIDAY DECRATINS During the holiday season, 13 homes on a certain street displayed lights and 8 displayed lawn ornaments. Five of the homes displayed both lights and lawn ornaments. If there are 32 homes on the street, how many had no decorations at all? 5. LUNCHTIME At the local high school, 240 students reported they have eaten the cafeteria's hot lunch, 135 said they have eaten the cold lunch, and 82 said they have eaten both the hot and cold lunch. If there are 418 students in the school, how many bring lunch from home? Chapter 3 24 Course 3
3-3 NAME Practice DATE PERID Problem-Solving Investigation: Use a Venn Diagram Mied Problem Solving Use a Venn diagram to solve Eercises 1 and 2. 1. SPRTS f the 25 baseball players on the Baltimore rioles 2005 roster, 17 threw right handed, 12 were over 30 years old, and 9 both threw right handed and were over 30 years old. How many players on the team neither threw right handed nor were over 30 years old? 4. GEGRAPHY f the 50 U.S. states, 30 states border a major body of water and 14 states border a foreign country. Seven states border both a major body of water and a foreign country. How many states border on just a major body of water and how many border on just a foreign country? 2. GRADES The principal noticed that 45 students earned As in English, 49 students earned As in math, and 53 students earned As in science. f those who earned As in eactly two of the subjects, 8 earned As in English and math, 12 earned As in English and science, and 18 earned As in math and science. Seventeen earned As in all three subjects. How many earned As in English only? Use any strategy to solve Eercises 3 6. Some strategies are shown below. PRBLEM-SLVING STRATEGIES Look for a pattern. Use a Venn diagram. Guess and check. 3. NUMBERS What are the net two numbers in the pattern? 486, 162, 54, 18,, 5. LANDSCAPING Three different landscaping companies treat lawns for weeds. Company A charges $35 per treatment and requires 3 treatments to get rid of weeds. Company B charges $30 per treatment and requires 4 treatments. Company C charges $50 per treatment and requires only two treatments to eliminate weeds. If you want to use the company that charges the least, which company should you choose? 6. RECEIVING Marc unloaded 7,200 bottles of water from delivery trucks today. If each truck contained 50 cases and each case contained 24 bottles of water, how many trucks did he unload? Lesson 3 3 Chapter 3 25 Course 3
3-3 Word Problem Practice Problem-Solving Investigation: Use a Venn Diagram Use a Venn diagram to solve each problem. NATINAL PARKS For Eercises 1 and 2, use the information in the bo. It shows the number of people who visited two National Parks in one year. Number of Yearly Pass Holders Who Pass Holders Who Pass Holders National Park Visited Yellowstone Visited Yosemite Who Visited Passes Sold National Park National Park Both Parks 4,250,000 1,420,000 2,560,000 770,000 1. How many yearly pass holders visited NLY Yellowstone Park? 2. How many yearly pass holders did not visit either Yosemite Park or Yellowstone Park? 3. PIZZA At a skating party, 10 skaters said they like pepperoni on their pizza, 12 said they like sausage. Seven skaters said they like both, and the rest like plain cheese. If there were 20 skaters having pizza, how many like plain cheese? 5. BKS f the 420 people who visited the library, 140 people checked out a nonfiction book, 270 checked out a fiction book. Ninety-five of the visitors checked out both fiction and nonfiction. How many visitors did not check out a book? 4. FIELD TRIP f the 24 students on a fieldtrip to the local ski hill, 13 ski and 11 snowboard. Four of the students ski and snowboard. How many students do not ski or snowboard? 6. SIBLINGS f the 18 girls on a soccer team, 10 have a sister, 14 have a brother, and 8 have both a brother and a sister. How many of the girls do not have a brother or a sister? Chapter 3 26 Course 3
3-4 NAME DATE PERID Study Guide and Intervention The Real Number System Numbers may be classified by identifying to which of the following sets they belong. Whole Numbers Integers Rational Numbers Irrational Numbers 0, 1, 2, 3, 4,, 2, 1, 0, 1, 2, numbers that can be epressed in the form a, where a and b are b integers and b 0 numbers that cannot be epressed in the form a, where a and b are b integers and b 0 Eamples Name all sets of numbers to which each real number belongs. 5 whole number, integer, rational number 0.666 25 11 Decimals that terminate or repeat are rational numbers, since they can be epressed as fractions. 0.666 2 3 Since 25 5, it is an integer and a rational number. 11 3.31662479 Since the decimal does not terminate or repeat, it is an irrational number. To compare real numbers, write each number as a decimal and then compare the decimal values. Eample 5 Replace with,, or to make 2 1 4 Write each number as a decimal. 2 1 2.25 4 5 2.236067 Since 2.25 is greater than 2.236067, 2 1 5. 4 Eercises Name all sets of numbers to which each real number belongs. 1. 30 2. 11 3. 5 4 4. 21 7 5 a true sentence. 5. 0 6. 9 7. 6 8. 101 3 Replace each with,, or to make a true sentence. 9. 2.7 7 10. 11 3 1 2 11. 4 1 17 12. 3.8 15 6 Chapter 3 28 Course 3
3-4 Skills Practice The Real Number System Name all sets of numbers to which each real number belongs. 1. 12 2. 15 3. 1 1 4. 3.18 2 5. 8 6. 9.3 4 7. 2 7 8. 25 9 9. 3 10. 64 11. 12 12. 13 Estimate each square root to the nearest tenth. Then graph the square root on a number line. 13. 5 14. 14 1 2 3 4 15. 6 16. 13 4 3 2 1 Replace each with,, or to make a true sentence. 17. 1.7 3 18. 6 2 1 2 1 2 3 4 4 3 2 1 19. 4 2 19 20. 4.8 24 5 Lesson 3 4 21. 6 1 38 22. 55 7.42 6 23. 2.1 4.41 24. 2.7 7.7 Chapter 3 29 Course 3
3-4 Practice The Real Number System Name all sets of numbers to which the real number belongs. 8 1. 9 2. 1 4 4 3. 3 5 4. 1 1 5. 9.55 6. 5.3 7. 2 0 5 8. 4 4 Estimate each square root to the nearest tenth. Then graph the square root on a number line. 9. 7 10. 1 9 11. 3 3 Replace each with,, or to make a true sentence. 12. 8 2.7 13. 1 5 3.9 14. 5 2 3 0 5 3 15. 2 5.2 9 16. 9.8 3.1 17. 8.2 8 2 1 0 9 rder each set of numbers from least to greatest. 18. 1 0, 8, 2.75, 2.8 19. 5.01, 5.01, 5.0 1, 2 6 20. 1 2, 1 3, 3.5, 3.5 21. ALGEBRA The geometric mean of two numbers a and b is a b. Find the geometric mean of 32 and 50. 22. ART The area of a square painting is 600 square inches. To the nearest hundredth inch, what is the perimeter of the painting? Chapter 3 30 Course 3
3-4 Word Problem Practice The Real Number System 1. GEMETRY If the area of a square is 33 square inches, estimate the length of a side of the square to the nearest tenth of an inch. 2. GARDENING Hal has a square garden in his back yard with an area of 210 square feet. Estimate the length of a side of the garden to the nearest tenth of a foot. 3. ALGEBRA Estimate the solution of a 2 21 to the nearest tenth. 4. ALGEBRA Estimate the solution of b 2 67.5 to the nearest tenth. 5. ARITHMETIC The geometric mean of two numbers a and b can be found by evaluating a. b Estimate the geometric mean of 4 and 11 to the nearest tenth. 7. GEMETRY The length s of a side of a cube is related to the surface area A of the cube by the formula s A 6. If the surface area is 27 square inches, what is the length of a side of the cube to the nearest tenth of an inch? 6. ELECTRICITY In a certain electrical circuit, the voltage V across a 20 ohm resistor is given by the formula V 20P, where P is the power dissipated in the resistor, in watts. Estimate to the nearest tenth the voltage across the resistor if the power P is 4 watts. 8. PETS Alicia and Ella are comparing the weights of their pet dogs. Alicia reports that her dog weighs 11 1 5 pounds, while Ella says that her dog weighs 125 pounds. Whose dog weighs more? Lesson 3 4 Chapter 3 31 Course 3
3-5 Study Guide and Intervention The Pythagorean Theorem The Pythagorean Theorem describes the relationship between the lengths of the legs of any right triangle. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. You can use the Pythagorean Theorem to find the length of a side of a right triangle if the lengths of the other two legs are known. Eamples Find the missing measure for each right triangle. Round to the nearest tenth if necessary. 24 ft c 20 cm 15 cm c 2 a 2 b 2 c 2 a 2 b 2 c 2 24 2 32 2 20 2 15 2 b 2 c 2 576 1,024 400 225 b 2 c 2 1,600 400 225 225 b 2 225 c 1,600 175 b 2 c 40 or 40 175 b 2 13.2 b Length must be positive, so the length of the hypotenuse is 40 feet. Eercises The length of the other leg is about 13.2 centimeters. Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. 1. 2. 3. 4 ft c 5 ft 32 ft c 9 m b 5 m 25 in. 15 in. a 4. a 7 km, b 12 km 5. a 10 yd, c 25 yd 6. b 14 ft, c 20 ft Chapter 3 34 Course 3
3-5 NAME DATE PERID Skills Practice The Pythagorean Theorem Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. 1. 2. 3. 10 m c 8 in. 5 m 3 cm a 7 in. b 11 cm 4. 18 ft 5. 6. c 15 ft 24 yd 30 yd 20 ft b a 13 ft 7. a 1 m, b 3 m 8. a 2 in., c 5 in. 9. b 4 ft, c 7 ft 10. a 4 km, b 9 km 11. a 10 yd, c 18 yd 12. b 18 ft, c 20 ft 13. a 5 yd, b 11 yd 14. a 12 cm, c 16 cm 15. b 22 m, c 25 m 16. a 21 ft, b 72 ft 17. a 36 yd, c 60 yd 18. b 25 mm, c 65 mm Determine whether each triangle with sides of given lengths is a right triangle. 19. 10 yd, 15 yd, 20 yd 20. 21 ft, 28 ft, 35 ft 21. 7 cm, 14 cm, 16 cm 22. 40 m, 42 m, 58 m 23. 24 in., 32 in., 38 in. 24. 15 mm, 18 mm, 24 mm Lesson 3 5 Chapter 3 35 Course 3
3-5 Practice The Pythagorean Theorem Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. 1. 2. 3. 26 in. a in 8 ft 10 ft 24 in. c cm 18 cm 15 cm b ft a yd 4. 5. 6. c mm 14 yd 50 mm 28 yd 50 mm c m 64 m 45 m 7. a, 65 cm; c, 95 cm 8. a, 16 yd; b, 22 yd Determine whether each triangle with sides of given lengths is a right triangle. 9. 18 ft, 23 ft, 29 ft 10. 7 yd, 24 yd, 25 yd 11. The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. Find the length of the other leg. 12. A leg of a right triangle is 30 meters long, and the hypotenuse is 35 meters long. What is the length of the other leg? 13. TELEVISINS The diagonal of a 27-inch television measures 27 inches. If the width of a 27-inch is 22 inches, calculate its height to the nearest inch. Chapter 3 36 Course 3
3-5 Word Problem Practice The Pythagorean Theorem 1. ART What is the length of a diagonal of a rectangular picture whose sides are 12 inches by 17 inches? Round to the nearest tenth of an inch. 2. GARDENING Ross has a rectangular garden in his back yard. He measures one side of the garden as 22 feet and the diagonal as 33 feet. What is the length of the other side of his garden? Round to the nearest tenth of a foot. 3. TRAVEL Troy drove 8 miles due east and then 5 miles due north. How far is Troy from his starting point? Round the answer to the nearest tenth of a mile. 4. GEMETRY What is the perimeter of a right triangle if the hypotenuse is 15 centimeters and one of the legs is 9 centimeters? 5. ART Anna is building a rectangular picture frame. If the sides of the frame are 20 inches by 30 inches, what should the diagonal measure? Round to the nearest tenth of an inch. 7. CNSTRUCTIN A door frame is 80 inches tall and 36 inches wide. What is the length of a diagonal of the door frame? Round to the nearest tenth of an inch. 6. CNSTRUCTIN A 20-foot ladder leaning against a wall is used to reach a window that is 17 feet above the ground. How far from the wall is the bottom of the ladder? Round to the nearest tenth of a foot. 8. TRAVEL Tina measures the distances between three cities on a map. The distances between the three cities are 45 miles, 56 miles, and 72 miles. Do the positions of the three cities form a right triangle? Lesson 3 5 Chapter 3 37 Course 3
3-6 NAME DATE PERID Study Guide and Intervention Using the Pythagorean Theorem You can use the Pythagorean Theorem to help you solve problems. Eample 1 A professional ice hockey rink is 200 feet long and 85 feet wide. What is the length of the diagonal of the rink? c 85 ft c 2 a 2 b 2 The Pythagorean Theorem 200 ft c 2 200 2 85 2 Replace a with 200 and b with 85. c 2 40,000 7,225 Evaluate 200 2 and 85 2. c 2 47,225 c 2 47,22 5 c 217.3 Simplify. Take the square root of each side. Simplify. The length of the diagonal of an ice hockey rink is about 217.3 feet. Eercises Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary. 1. What is the length of the diagonal? 2. How long is the kite string? 6 in. c c 30 m 6 in. 25 m 3. How high is the ramp? 4. How tall is the tree? 15 ft b 18 yd h 10 ft 7 yd Chapter 3 40 Course 3
3-6 NAME DATE PERID Skills Practice Using the Pythagorean Theorem Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary. 1. How far apart are the spider and 2. How long is the tabletop? the fly? table 6 ft 3 ft Lesson 3 6 2 ft c 3 ft 3. How high will the ladder reach? 4. How high is the ramp? 17 ft h 16 ft h 15 ft 4 ft 5. How far apart are the two cities? 6. How far is the bear from camp? c Lakeview 20 yd 60 yd 41 mi d camp Avon 19 mi 7. How tall is the table? table 8. How far is it across the pond? d h 40 in. 75 m 90 m 30 in. Chapter 3 41 Course 3
3-6 Practice Using The Pythagorean Theorem Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary. 1. How far is the ship from 2. How long is the wire 3. How far above the water is the lighthouse? supporting the sign? the person parasailing? 6 mi 8 mi d 1.5 ft w 2 ft pen 24/7 100 yd p 80 yd 4. How wide is the pond? 5. How high is the ramp? 6. How high is the end of the ladder against the building? 95 ft 120 ft w 19 ft 21 ft 7. GEGRAPHY Suppose Birmingham, Huntsville, and Gadsden, Alabama, form a right triangle. What is the distance from Huntsville to Gadsden? Round to the nearest tenth if necessary. 8. GEMETRY Find the diameter d of the circle in the figure at the right. Round to the nearest tenth if necessary. h h 13 ft 4 ft Huntsville 98 mi Gadsden 61 mi Birmingham 18 ft d 22 ft Chapter 3 42 Course 3
3-6 Word Problem Practice Using the Pythagorean Theorem 1. RECREATIN A pool table is 8 feet long and 4 feet wide. How far is it from one corner pocket to the diagonally opposite corner pocket? Round to the nearest tenth. 2. TRIATHLN The course for a local triathlon has the shape of a right triangle. The legs of the triangle consist of a 4-mile swim and a 10-mile run. The hypotenuse of the triangle is the biking portion of the event. How far is the biking part of the triathlon? Round to the nearest tenth if necessary. Lesson 3 6 3. LADDER A ladder 17 feet long is leaning against a wall. The bottom of the ladder is 8 feet from the base of the wall. How far up the wall is the top of the ladder? Round to the nearest tenth if necessary. 4. TRAVEL Tara drives due north for 22 miles then east for 11 miles. How far is Tara from her starting point? Round to the nearest tenth if necessary. 5. FLAGPLE A wire 30 feet long is stretched from the top of a flagpole to the ground at a point 15 feet from the base of the pole. How high is the flagpole? Round to the nearest tenth if necessary. 6. ENTERTAINMENT Isaac s television is 25 inches wide and 18 inches high. What is the diagonal size of Isaac s television? Round to the nearest tenth if necessary. Chapter 3 43 Course 3
3-7 Study Guide and Intervention Distance on the Coordinate Plane You can use the Pythagorean Theorem to find the distance between two points on the coordinate plane. Eample Find the distance between points (2, 3) and (5, 4). Graph the points and connect them with a line segment. Draw a horizontal line through (2, 3) and a vertical line through (5, 4). The lines intersect at (5, 3). Count units to find the length of each leg of the triangle. The lengths are 3 units and 7 units. Then use the Pythagorean Theorem to find the hypotenuse. c 2 a 2 b 2 The Pythagorean Theorem c 2 3 2 7 2 Replace a with 3 and b with 7. c 2 9 49 Evaluate 3 2 and 7 2. c 2 58 Simplify. c 2 58 c 7.6 Simplify. Take the square root of each side. The distance between the points is about 7.6 units. y (5, 4) 7 units (5, 3) (2, 3) 3 units Lesson 3 7 Eercises Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary. 1. y 2. y 3. (6, 3) (4, 3) (1, 1) Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth if necessary. 4. (4, 5), (0, 2) 5. (0, 4), ( 3, 0) 6. ( 1, 1), ( 4, 4) y ( 2, 1) y y y (1, 1) (3, 2) Chapter 3 47 Course 3
3-7 Skills Practice Distance on the Coordinate Plane Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary. 1. 2. 3. y y y ( 3, 2) (0, 1) ( 1, 2) (4, 2) (2, 1) ( 2, 1) 4. 5. 6. y (5, 6) (3, 3) ( 2, 2) (2, 3) y y (1, 1) (4, 3) Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth if necessary. 7. ( 3, 0), (3, 2) 8. ( 4, 3), (2, 1) 9. (0, 2), (5, 2) y 10. ( 2, 1), ( 1, 2) 11. (0, 0), ( 4, 3) 12. ( 3, 4), (2, 3) y y y y y Chapter 3 48 Course 3
3-7 Practice Distance on the Coordinate Plane Name the ordered pair for each point. 1. A 2. B F 3. C 4. D B E A 5. E 6. F 7. G 8. H Graph and label each point. H G C D Lesson 3 7 9. J 2 1 4, 1 2 10. K 3, 1 2 3 11. M 3 3 4, 4 1 4 12. N 3 2 5, 2 3 5 13. P 2.1, 1.8 14. Q 1.75, 3.5 Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth if necessary. 15. (4, 3), (1, 1) 16. (3, 2), (0, 4) 17. ( 4, 3.5), (2, 1.5) 18. Find the distance between points R and S shown at the right. Round to the nearest tenth. y S 19. GEMETRY If one point is located at ( 6, 2) and another point is located at (6, 3), find the distance between the points. 0 R Chapter 3 49 Course 3
3-7 Word Problem Practice Distance on the Coordinate Plane 1. ARCHAELGY An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found one at position (1, 4) and the other at (5, 2). How far apart were the two artifacts? Round to the nearest tenth of a unit if necessary. 2. GARDENING Vega set up a coordinate system with units of feet to locate the position of the vegetables she planted in her garden. She has a tomato plant at (1, 3) and a pepper plant at (5, 6). How far apart are the two plants? Round to the nearest tenth if necessary. 3. CHESS April is an avid chess player. She sets up a coordinate system on her chess board so she can record the position of the pieces during a game. In a recent game, April noted that her king was at (4, 2) at the same time that her opponent s king was at (7, 8). How far apart were the two kings? Round to the nearest tenth of a unit if necessary. 4. MAPPING Cory makes a map of his favorite park, using a coordinate system with units of yards. The old oak tree is at position (4, 8) and the granite boulder is at position ( 3, 7). How far apart are the old oak tree and the granite boulder? Round to the nearest tenth if necessary. 5. TREASURE HUNTING Taro uses a coordinate system with units of feet to keep track of the locations of any objects he finds with his metal detector. ne lucky day he found a ring at (5, 7) and an old coin at (10, 19). How far apart were the ring and coin before Taro found them? Round to the nearest tenth if necessary. 7. GEMETRY The coordinates of points A, B, and C are (5, 4), ( 2, 1), and (4, 4), respectively. Which point, B or C, is closer to point A? 6. GEMETRY The coordinates of points A and B are ( 7, 5) and (4, 3), respectively. What is the distance between the points, rounded to the nearest tenth? 8. THEME PARK Tom is looking at a map of the theme park. The map is laid out in a coordinate system. Tom is at (2, 3). The roller coaster is at (7, 8), and the water ride is at (9, 1). Is Tom closer to the roller coaster or the water ride? Chapter 3 50 Course 3
3-7 Spreadsheet Activity Distance on the Coordinate Plane You can use a spreadsheet to calculate the distance between two points on a coordinate plane. Eample Use a spreadsheet to find the distance between ( 3, 2) and (4, 6). Round to the nearest hundredth. Step 1 Step 2 Use the cell A1 for the -coordinate of the first point and cell B1 for the y-coordinate of the first point. Enter the -coordinate of the second point in cell C1 and the y-coordinate of the second point in cell D1. In cell E1, enter an equals sign followed by the formula for the distance. The formula is SQRT((C1-A1)^2 (D1- B1)^2). Then press ENTER to return the distance between the two points. The distance between ( 3, 2) and (4, 6) is about 8.06 units. Find the following distances. Round to the nearest hundredth. 1 2 3 4 5 6 7 1. (2, 3) and ( 1, 3) 2. (5, 2) and ( 2, 7) 3. ( 3, 1) and (7, 9) 4. (4, 5) and ( 7, 2) 5. (9, 2) and ( 7, 1) 6. (8, 2) and ( 1, 5) 7. (0, 3) and ( 2, 3) 8. ( 7, 3) and ( 6, 2) 9. (9, 2) and ( 5, 2) 10. (3, 3) and ( 2, 5) 11. ( 1, 2) and (1, 9) 12. (0, 5) and ( 1, 2) A B C D E -3 2 4 6 8.062258 Sheet 1 Sheet 2 Sheet 3 13. (5, 3) and (0, 3) 14. (1, 2) and (7, 3) 15. (5, 1) and ( 2, 3) 16. (7, 3) and (2, 3) 17. (7, 2) and (6, 0) 18. (1, 3) and (7, 2) Chapter 3 52 Course 3
3 NAME DATE PERID Chapter 3 Vocabulary Test abscissa converse coordinate plane hypotenuse irrational number legs ordered pair ordinate origin perfect square Pythagorean Theorem quadrants radical sign real number square root -ais -coordinate y-ais y-coordinate Choose from the terms above to complete each sentence. 1. The is the vertical number line in the 1. coordinate plane. 2. A real number that cannot be epressed as a decimal that 2. terminates or repeats is called a(n). 3. The sides of a right triangle that form a 90 angle are 3. called. 4. The first number in an ordered pair is the -coordinate or 4.. 5. The is the horizontal number line in the 5. coordinate plane. 6. The of the Pythagorean Theorem states 6. that if the sides of a triangle have lengths a, b, and c units such that c 2 a 2 b 2, then the triangle is a right triangle. 7. The set of contains the set of rational 7. numbers. 8. The of a right triangle is always the 8. longest side of the triangle. 9. The second number in an ordered pair is the y-coordinate 9. or. 10. The point where the zero points of the two number lines 10. meet at right angles in the coordinate plane is called the. Define each term in your own words. 11. Pythagorean Theorem 11. 12. Pythagorean triple 12. Chapter 3 58 Course 3
3 Chapter 3 Test, Form 1 (continued) 12. Which set of numbers is ordered from least to greatest? F. 16, 17, 18, 9 H. 5, 6, 2 1, 3 2 G. 2.8 2, 8, 11, 3 1 J. 10, 4, 4, 1.5 12. 2 For Questions 13 15, find the length of the missing side of each right triangle. Round to the nearest tenth if necessary. 13. a 9 feet, b 12 feet b A. 7.9 ft C. 4.6 ft B. 1.7 ft D. 15 ft a c 13. 14. a 2 centimeters, c 5 centimeters F. 1.7 cm G. 5.4 cm H. 4.6 cm J. 2.6 cm 14. 15. a 3 inches, b 6 inches A. 3 in. B. 4.2 in. C. 6.7 in. D. 5.2 in. 15. 16. REAL ESTATE José s yard is 30 meters by 40 meters. What is the distance from one corner to the opposite corner? F. 8.4 m G. 70 m H. 50 m J. 26.5 m 16. 17. EXERCISE Sandy walked 2 miles south and then walked 4 miles east. How far was Sandy from her starting point? Round to the nearest tenth. A. 4.5 mi B. 3.5 mi C. 6.0 mi D. 3.0 mi 17. Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary. 18. the points in the graph at the right F. 7 units H. 1 unit G. 7.8 units J. 3.3 units 18. 19. (2, 5), (5, 1) A. 8.1 units C. 2.7 units B. 25 units D. 5 units 19. 20. ( 3, 4), ( 2, 1) ( 3, 1) F. 6.4 units G. 25 units H. 2.6 units J. 5.1 units 20. y (3, 4) Bonus SWIMMING Marina is swimming in a rectangular pool B: that is 36 feet wide and 48 feet long. How much farther will she swim if she swims diagonally across the pool than if she swims the length of the pool? Chapter 3 60 Course 3
3 Chapter 3 Test, Form 2A SCRE Write the letter for the correct answer in the blank at the right of each question. For Questions 1 3, find each square root. 1. 225 A. 22.5 B. 15 C. 15 D. 14 1. 2. 1 44 10 0 F. 2 0 12 G. 3 5 H. 6 5 J. 5 2. 3 3. 2.56 A. 25.6 B. 1.6 C. 16 D. 0.256 3. 4. Solve v 2 576. F. 25 G. 24 or 24 H. 23 or 23 J. 24 4. For Questions 5 and 6, estimate to the nearest whole number. 5. 131 A. 12 B. 11 C. 10 D. 13 5. Assessment 6. 214 F. 15 G. 16 H. 13 J. 14 6. 7. SPRTS A survey of 12 students showed that 7 liked football, 10 liked basketball, and 5 liked both. How many students liked just basketball? A. 12 B. 10 C. 5 D. 2 7. 8. ALGEBRA Estimate the solution of b 2 52 to the nearest integer. F. 26 or 26 G. 26 H. 7 J. 7 or 7 8. 9. To which set(s) of numbers does 0.7 belong? A. rational C. irrational B. integer, whole, rational D. rational, integer 9. 10. To which set(s) of numbers does 2 7 belong? 3 F. whole H. irrational 10. G. integer, rational J. whole, integer, rational 11. Which is a true statement? A. 12 3 1 2 B. 2 1 5 5 C. 9 1 6 4 D. 15 3.9 11. Chapter 3 61 Course 3
3 Chapter 3 Test, Form 3 SCRE For Questions 1 3, find each square root. 1. 2,500 1. 2. 1 44 16 9 2. 3. 4.41 3. 4. Solve the equation r 2 4.84. 4. 5. Find a number that when squared equals 5.5696. 5. Estimate to the nearest whole number. 6. 154.5 6. 7. 59 7. 8. CLRS Draw a Venn diagram to show the following situation. In a survey of 47 people, 18 liked red, 13 liked orange, 16 liked yellow, 4 liked red and orange, 6 liked red and yellow, 3 liked orange and yellow, and 1 liked all three. 8. Assessment ALGEBRA Estimate the solution of each equation to the nearest integer. 9. e 2 66.5 9. 10. t 2 105 10. For Questions 11 and 12, name all sets of numbers to which each real number belongs. 11. 37 11. 12. 652 12. 13. Estimate 209 to the nearest tenth. Then 13. graph the square root on a number line. 15 14 13 12 14. rder 53, 7 1, 7.6, and 50 from least to greatest. 14. 8 Chapter 3 69 Course 3
3 Chapter 3 Test, Form 3 (continued) Write an equation you could use to find the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. 15. a 1.7 centimeters; c 2.2 centimeters 15. 16. b 36 millimeters; c 39 millimeters 16. For Questions 17 and 18, determine whether a triangle with sides of the given lengths is a right triangle. 17. 24 meters, 45 meters, 51 meters 17. 18. 48 feet, 69 feet, 92 feet 18. 19. LADDER A 16-foot ladder is leaning against a house, 19. touching the house at a height of 12 feet. How far away from the house is the base of the ladder? Round to the nearest tenth. 20. TULIPS Samuel has a garden that is shaped like a right 20. triangle. ne leg is 15 feet long, and the hypotenuse is 19 feet long. He has a limited number of tulip bulbs that he wants to plant. How many more feet will he have to cover if he plants them along the two legs rather than along the hypotenuse? Use a diagram and round to the nearest tenth. 21. TATAMIS The floors of houses in Japan are traditionally 21. covered by tatamis. Tatamis are rectangular-shaped straw mats that measure 6 feet by 3 feet. If a room is 8 tatamis by 8 tatamis, what is the distance in feet from one corner to the opposite corner? Use a diagram and round to the nearest tenth. Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary. 22. y 23. (5, 0), (2, 4) 22. ( 5, 2) 24. ( 2, 2), (1, 3) 25. ( 3, 2), (4, 2) 23. 24. (5, 2) 25. Bonus GEMETRY The formula for the area of a triangle is B: 1 bh. Find the area of a right triangle with a hypotenuse 2 length of 13 inches and one leg length of 5 inches. Chapter 3 70 Course 3
NAME: PERIDS: DATE TIME UT DESTINATIN RETURN SIGNATURE
NAME: PERIDS: DATE TIME UT DESTINATIN RETURN SIGNATURE