Assignment Assignment for Lesson.1 Name Date Get Radical or (Be)! Radicals and the Pythagorean Theorem Simplify the radical expression. 1. 60. 60 4 15 15. 8x 5 4. 8x 5 4 7 x x x x 7x 108 108 6 6 45x y 7 45x y 7 9 5 x x y y y y xy 5xy 1 5. 6. 49 1 49 1 7 4 7. 8. 6 6 6 6 6 6 6 6 6 6 1 1 1 6 1 1 144 6 1 1 009 Carnegie Learning, Inc. 9. A plane takes off from an airport and travels 4 miles due west and then 60 miles due north, landing on an island. How far is the airport from the island? 60 miles 4 miles d 60 4 d 600 576 d 4176 d 64.6 The airport is about 64.6 miles from the island. Chapter Assignments 7
10. A bird leaves its nest and flies two miles due north, then three miles due east, then four miles due north, and then five miles due east, finally reaching the ocean. How far is the bird s nest from the ocean? mi 4 mi 5 mi mi d 6 8 d 6 64 d 100 d 10 The nest is 10 miles from the ocean. 11. Two friends leave Pittsburgh at the same time in separate cars. One car travels due east, while the other car travels due north. Both cars travel at 55 miles per hour. Each car has a two-way radio with a talking range of 400 miles. In how many hours will they be too far apart to communicate on their radios? d d 400 55t 8.84 d 160,000 t 5.14 d 80,000 d 8.84 They will be too far apart to communicate after about 5.14 hours. 1. A tree was planted 15.9 feet from a house and eventually grew to a height of feet. During an electrical storm, lightning struck the tree, causing the top of the tree to break off 6 feet above the ground. If the severed part of the tree is falling toward the house, will it hit the house? Explain your reasoning. Because the tree breaks off 6 feet from the ground, that leaves 6 17 feet of the tree to fall toward the house. If the house is only 15.9 feet away, then the tree will hit the house. The Pythagorean Theorem is not necessary to solve this problem. 1. What is the length of the longest side of the trapezoid shown? 5 miles 6 miles 9 miles d 5 9 d 5 81 d 56 d 7.48 Total length 6 7.48 The length of the longest side is 1.48 miles. 1.48 009 Carnegie Learning, Inc. 74 Chapter Assignments
Name Date 14. A boat drops an anchor with a 00-foot chain. The lake is 75 feet deep. How far can the boat drift in any one direction? d 75 00 d 565 40,000 d 4,75 d 185.40 The boat can drift about 185.4 feet in any one direction. 009 Carnegie Learning, Inc. Chapter Assignments 75
009 Carnegie Learning, Inc. 76 Chapter Assignments
Assignment Assignment for Lesson. Name Date The Pythagorean Theorem Disguised as the Distance Formula! The Distance Formula and Midpoint Formula Ben is playing soccer with his friends Abby and Clay. Their positions on the soccer field are represented in the following graph. Each interval is measured in meters. Use the coordinates on the graph to answer Questions 1 through. y 11 10 9 8 7 6 5 4 1 Ben Abby Clay 1 4 5 6 7 8 9 10 11 x 1. How far does Abby have to kick the ball to Clay? 009 Carnegie Learning, Inc. d (11 ) (0 0) 8 0 64 0 64 8 Abby has to kick the ball 8 meters to Clay.. How far does Ben have to kick the ball to Abby? d ( 5) (0 9) 9 4 81 85 9. Ben has to kick the ball about 9. meters to Abby.. How far does Ben have to kick the ball to Clay? d (11 5) (0 9) 6 9 6 81 117 10.8 Ben has to kick the ball about 10.8 meters to Clay. 4. Find the distance between the points ( 10, 7) and (1, 17). d (1 ( 10)) (17 ( 7)) 4 59 576 1105.4 Chapter Assignments 77
5. The distance between the points (x, 5) and (0, ) is 10. What is x? d (0 x) ( ( 5)) x 8 x 64 x 64 10 x 64 100 x 6 x 6 6. The distance between the points ( 6, 0) and ( 9, y) is 65. What is y? d ( 9 ( 6)) (y 0) ( ) y 9 y 9 y 65 9 y 65 y 56 y 16 7. While playing in the sandbox, Sara sees her friend Tanya at the water fountain. The positions of the sandbox and the water fountain are represented in the following graph. Suppose that Sara meets her friend Tanya halfway between the fountain and the sandbox. What are the coordinates of the point where they meet? sandbox y 1 11 10 9 8 7 6 5 4 1 fountain 009 Carnegie Learning, Inc. 5 4 1 1 1 4 5 6 7 8 9 x ( x 1 x, y 1 y ) ( The coordinates of the point where they meet are (, 8). 78 Chapter Assignments 1 7, 10 6 ) ( 6, 16 (, 8) )
Name Date In Questions 8 through 10, determine the midpoint of the line segment with the given endpoints. 8. (, 5) and (4, 1) ( x 1 x, y 1 y ) ( 9. (4, ) and (, 5) ( x 1 x, y 1 y ) ( 10. (, 4) and (, 7) ( x 1 x, y 1 y ) ( 4, 5 1 ) (, 6 (1, ) ) 4 ( ),, ( 5) ) (, (1, 1) ) 4 ( 7) ) ( 0, 11 ) ( 0, 11 ) 11. The midpoint of a line segment is (, 1) and one endpoint of the segment is (, ). What is the other endpoint? x x 4 x 1 The other endpoint is (1, 4). y 1 y y 4 009 Carnegie Learning, Inc. Chapter Assignments 79
009 Carnegie Learning, Inc. 80 Chapter Assignments
Assignment Assignment for Lesson. Name Date Drafting Equipment Properties of 45-45 -90 Triangles 1. The legs of the isosceles triangle each measure 14 inches. Find the length of the hypotenuse. 14 in. 45 c The length of the hypotenuse is 14 or about 19.80 inches. 45 14 in.. Find the value of c. 45 c 7 ft The value of c is 7 14 feet. 45 7 ft 009 Carnegie Learning, Inc.. The perimeter of the square is centimeters. Find the length of its diagonal. side 8 cm 4 The diagonal is 8 or about 11.1 centimeters. 4. Find the value of a. 1 m a a 1 The value of a is 1 meters. Chapter Assignments 81
5. The length of a diagonal of the square is 6 centimeters. Find the length of each side. 6 cm 6 Each side is 5.46 centimeters. 6. The diagonal of the square is 1 centimeters. Find the area. 1 cm side 1 area ( 1 ) 7 cm The area of the square is 7 square centimeters. 7. Find the area of the following figure using the information given in the diagram. The figure is composed of a triangle and a semicircle. Use.14 for. 1 cm 1 cm area of triangle 1 (1)(1) 7 cm diameter of circle 1 cm radius of circle 6 cm area of semicircle 1 (6 ) 6 cm Total area 7 6 185.04 cm 8. The diagonal of the square in the following figure is 60 inches. Find the perimeter of the figure. The figure is composed of a square and a semicircle. s 60 60 in. 009 Carnegie Learning, Inc. three sides 180 circumference of semicircle perimeter 180 0 1 ( 60 0 ) 19.89 in. 8 Chapter Assignments
Assignment Assignment for Lesson.4 Name Date Finishing Concrete Properties of 0-60 -90 Triangles 1. The measure of the hypotenuse in the following 0º-60º-90º triangle is 8 meters. Find the length of sides a and b. a 60 8 m shorter leg: longer leg: a 8 a 14 m b a 14 4.5 m b 0. The measure of the side opposite the 0º angle is 5 feet. Find the length of sides b and c. b 0 c longer leg: b a 5 8.66 ft hypotenuse: c a 10 ft 60 5 ft 009 Carnegie Learning, Inc.. The measure of the side opposite the 60º angle is 8 millimeters. Find the length of sides a and c. a 60 c 8 mm 0 shorter leg: a b a 8 a 8 a 4.6 mm 8 hypotenuse: c a ( ) 16 9.4 mm Chapter Assignments 8
4. A broadcast antenna is situated on top of a tower. The signal travels from the antenna to your house so you can watch TV. The angle of elevation from your house to the tower measures 0 and the distance from your house to the tower is 500 feet. Find the height of the tower and the distance the signal travels. Antenna 60 0 500 feet House The height of the tower is the short leg. long leg short leg 500 88.68 feet The height of the tower is about 88.68 feet. hypotenuse short leg 577.6 feet The distance the signal travels is about 577.6 feet. 5. The measure of the longer leg in the following 0º-60º-90º triangle is miles. Find the length of the hypotenuse. 60 0 miles short leg 1.70 hypotenuse short leg 5.4 miles 6. The length of the shorter leg in the following 0º-60º-90º triangle is 1 meters. Find the length of the hypotenuse. 1 m 60 0 7. Find the perimeter of the trapezoid. 6 cm 60 60 14 cm hypotenuse short leg 1 6 meters Form a 0º-60º-90º right triangle as shown. short leg 14 6 4 cm hypotenuse 4 8 cm perimeter 14 6 8 8 6 cm 009 Carnegie Learning, Inc. 84 Chapter Assignments
Name Date 8. Find the area of the triangle. Split the triangle into two 0º-60º-90º triangles as shown. base 0 0 cm height 10 60 60 area 1 (0)(10 ) 100 or about 17. cm 9. Find the area of the trapezoid. 6 cm 8 cm 45 height of the trapezoid length of longer base 8 6 8 or about 5.66 cm or about 11.66 cm area of trapezoid 1 (11.66 6)(5.66) 49.98 cm 009 Carnegie Learning, Inc. 10. A broadcast antenna is situated on top of a tower, and the signal travels from the antenna to your house so that you can watch TV. The angle of elevation from your house to the tower measures 0º and the distance from your house to the tower is 775 feet. Find the height of the tower and the distance the signal travels. Antenna a 60 c 0 775 feet House The height of the tower is the short leg. The short leg is equal to the long leg divided by 775, or 447.45 feet. So, the height of the tower is about 447.45 feet. The hypotenuse is twice the length of the short leg or 447.45 894.9 feet. So, the signal travels a distance of about 894.9 feet. Chapter Assignments 85
009 Carnegie Learning, Inc. 86 Chapter Assignments