Pythagorean Theorem Applications Directions: Sketch a diagram, setup the corresponding equation, simplify, and solve. State solutions as both simplified square roots and an approximated decimal. 1. The owners of a house want to convert a stairway leading from the ground to their back porch into a ramp. The porch Is 3 feet off the ground, and due to building regulations, the ramp must start 12 feet away from the base of the porch. How long will the ramp be? 2. You're locked out of your house and the only open window is on the second floor, 30 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a flower garden along the edge of the house, so you'll have to place the ladder 12 feet from the house. What length of ladder do you need to reach the window? B. Tony needs go to the store from his home. He can either take the sidewalk all the way, walking 3 blocks north and 2 blocks east, or cut across the field at the corner. How much shorter is the trip if he cuts across the field? 4. A water park wants to add a zipline into a pool. If the platform at the top of the zipline is 25 feet tall, and the pool is 40 feet long, what is the maximum length needed for the zipline?5. In the right figure, Al . AD = 4, BC = 6 and CD = 20. The angle ADC and BCD are right angles. The point P is on the line CD. Find the of AP + BP. 6. What is the height of the isosceles triangle with side lengths of 9 and a base of 14? 7. Stanley is traveling from point A to point # by taking a shortcut through the pond. A path that avoids the pond is 25 feet south and 28 feet east. To the nearest tenth of a foot, how many feet will Stanley save by going through the pond instead of following the path?8. Given a square with an area of 49 square units, determine the length of the diagonal. 9. The front view of a tent measures 8 feet across the bottom and 5 feet on the slanted sides. What is the height of the tent, in feet, at its tallest point? 10. In right triangle, Am . 20 is a right angle, AB = 3v2 and AC = 2V15. Find BC. 11, An Isosceles triangle has side lengths of 16, an altitude of x. and a base of 2x. Find the length of the base.12. Dylan wants to get from point A to point C as quickly as possible. He can climb the stairs directly from A to Cat a rate of 10 meters per minute, or he can bike along the bike path from A to B to Cat the rate of 30 meters per minute. If AB is perpendicular to BC, AB = 90 meters, and BC = 120 meters, which route will get Dylan to point C in less time? 13. An equilateral triangle is plotted in the coordinate plane such that two of its vertices are (0,0) and (8,0). What are the coordinates of the third vertex? 14. Mary wants to get a computer monitor for her desk which can hold a monitor that is 16 inches wide and 10 inches high. Will a 22 inch monitor fit? 15. A cube has side lengths of 4. Determine the length of the diagonal of the cube.Special Right Triangles Copy and complete the following charts on your own paper - filling in the "?". Show your work for each equation. HINT: Use Pythagorean Theorem. 45-45-90 Triangles leg leg bypotenuse 3 ? 4 5 51/2 6 612 10 10 12 ? 12 1/2 25 25 ? 32 32 1/2 30-60-90 Triangles short leg long leg hypotenuse 3 ? 6 . 413 ? 5 10 ? 61/3 12 10 1013 ? 12 ? 24 25 25 V3 32 V/3 64Special Right Triangles Practice 45-45-90 3. G. 7. Find the perimeter of a square with diagonal 12 centimeters. B. Find the diagonal of a square with perimeter 20 inches. 9. Find the diagonal of a square with perimeter 28 meters, 30-60-90 1. 2. 3 5. 7. The perimeter of an equilateral triangle is 32 centimeters. Find the length of an altitude of the triangle 8. An altitude of an equilateral triangle is 18 meters. Find the perimeter of the triangle