Assignment Assignment for Lesson.1 Name Date Get Radical or (Be) 2! Radicals and the Pythagorean Theorem Simplify the radical expression. 1. 60 2. 108. 28x 5 4. 45x y 7 5. 1 49 6. 7. 6 8. 2 12 9. A plane takes off from an airport and travels 24 miles due west and then 60 miles due north, landing on an island. How far is the airport from the island? 60 miles 24 miles 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? 4 mi 5 mi 2 mi mi 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? 12. A tree was planted 15.9 feet from a house and eventually grew to a height of 2 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. 1. What is the length of the longest side of the trapezoid shown? 5 miles 6 miles 9 miles 74 Chapter Assignments
Name Date 14. A boat drops an anchor with a 200-foot chain. The lake is 75 feet deep. How far can the boat drift in any one direction? Chapter Assignments 75
76 Chapter Assignments
Assignment Assignment for Lesson.2 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 2 1 Ben Abby Clay 1 2 4 5 6 7 8 9 10 11 x 1. How far does Abby have to kick the ball to Clay? 2. How far does Ben have to kick the ball to Abby?. How far does Ben have to kick the ball to Clay? 4. Find the distance between the points ( 10, 7) and (1, 17). Chapter Assignments 77
5. The distance between the points (x, 5) and (0, ) is 10. What is x? 6. The distance between the points ( 6, 0) and ( 9, y) is 265. What is y? 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 12 11 10 9 8 7 6 5 4 2 1 fountain 5 4 2 1 1 2 1 2 4 5 6 7 8 9 x 78 Chapter Assignments
Name Date In Questions 8 through 10, determine the midpoint of the line segment with the given endpoints. 8. ( 2, 5) and (4, 1) 9. (4, ) and ( 2, 5) 10. (, 4) and (, 7) 11. The midpoint of a line segment is (2, 1) and one endpoint of the segment is (, 2). What is the other endpoint? Chapter Assignments 79
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 45 14 in. 2. Find the value of c. 45 c 7 2 ft 45 7 2 ft. The perimeter of the square is 2 centimeters. Find the length of its diagonal. 4. Find the value of a. 12 2 m a a Chapter Assignments 81
5. The length of a diagonal of the square is 6 centimeters. Find the length of each side. 6 cm 6. The diagonal of the square is 12 centimeters. Find the area. 12 cm 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. 12 cm 12 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. 60 in. 82 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 28 meters. Find the length of sides a and b. a 60 28 m b 0 2. The measure of the side opposite the 0º angle is 5 feet. Find the length of sides b and c. 0 b c 60 5 ft. 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 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 5. The measure of the longer leg in the following 0º-60º-90º triangle is 22 miles. Find the length of the hypotenuse. 60 0 22 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 84 Chapter Assignments
Name Date 8. Find the area of the triangle. 20 cm 60 60 9. Find the area of the trapezoid. 8 cm 6 cm 45 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 Chapter Assignments 85
86 Chapter Assignments