(8) Lesson 5.6 - Use the Pythagorean Theorem
- 1. Course 3, Lesson 5-6 Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. 1. 2. 3. 4. Is a triangle with side lengths of 18, 25, and 33 a right triangle? 5. A man drives 33 miles east and 12 miles south. What is the shortest distance between the man and his starting point?
- 2. Course 3, Lesson 5-6 ANSWERS 1. 32 + 42 = x2; 5 cm 2. 152 + x2 = 252; 20 ft 3. x2 + 122 = 132; 5 in. 4. no 5. 35
- 3. HOW can algebraic concepts be applied to geometry? Geometry Course 3, Lesson 5-6
- 4. Course 3, Lesson 5-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Geometry • 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. • 8.EE.2 Use square root cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.
- 5. Course 3, Lesson 5-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Geometry Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 7 Look for and make use of structure.
- 6. To • apply the Pythagorean Theorem to find unknown side lengths in right triangles in real-world situations, • use the Pythagorean Theorem to find missing measures in three-dimensional figures Course 3, Lesson 5-6 Geometry
- 7. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 1. Write an equation that can be used to find the length of the ladder. Then solve. Round to the nearest tenth. Pythagorean Theorema2 + b2 = c2 Replace a with 8.75 and b with 18. 76.5625 + 324 = c2 Notice that the distance from the building, the building itself, and the ladder form a right triangle. Use the Pythagorean Theorem. 8.752 + 182 = c2 Evaluate 8.752 and 182. 400.5625 = c2 Add 76.5625 and 324. Definition of square root Use a calculator.±20.0 ≈ c Since length cannot be negative, the ladder is about 20 feet long. ±√400.5625 = c
- 8. Answer Need Another Example? Write an equation that can be used to find the length of the boat ramp. Then solve. Round to the nearest tenth. 4.22 + 252 = c2; 25.4 ft
- 9. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 2. Write an equation that can be used to find the height of the plane. Then solve. Round to the nearest tenth. Pythagorean Theorema2 + b2 = c2 Replace a with 10 and c with 12. 100 + b2 = 144 The distance between the planes is the hypotenuse of a right triangle. Use the Pythagorean Theorem. 102 + b2 = 122 Evaluate 102 and 122. b2 = 44 Subtraction Property of Equality Since length cannot be negative, the height of the plane is about 6.6 miles. Definition of square root Use a calculator.b ≈ ±6.6 b = ±√44
- 10. Answer Need Another Example? Write an equation that can be used to find the length of the backboard. Then solve. Round to the nearest tenth. 422 + x2 = 83.42; 72.1 in.
- 11. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 3. A 12-foot flagpole is placed in the center of a square area. To stabilize the pole, a wire will stretch from the top of the pole to each corner of the square. The flagpole is 7 feet from each corner of the square. What is the length of each wire? Round to the nearest tenth. Pythagorean TheoremAB2 + AC2 = BC2 Replace AB with 7 and AC with 12. 49 + 144 = BC2 Draw right triangle ABC. You want to find the length of each wire or BC. This is the hypotenuse of a right triangle, so use the Pythagorean Theorem. 72 + 122 = BC2 Evaluate 72 and 122. 193 = BC2 Simplify Since length cannot be negative, the length of the wire is about 13.9 feet. Definition of square root Use a calculator.±13.9 ≈ BC ±√193 = BC
- 12. Answer Need Another Example? The slant height of a pyramid is the height of each lateral face. What is the slant height of the pyramid shown? Round to the nearest tenth. 11.7 cm
- 13. How did what you learned today help you answer the HOW can algebraic concepts be applied to geometry? Course 3, Lesson 5-6 Geometry
- 14. How did what you learned today help you answer the HOW can algebraic concepts be applied to geometry? Course 3, Lesson 5-6 Geometry Sample answer: • You write and solve equations using the Pythagorean Theorem to find missing lengths in real-world situations involving right triangles.
- 15. How do you think using the Pythagorean Theorem will connect with the next lesson about finding the distance between two points on the coordinate plane? Ratios and Proportional RelationshipsFunctionsGeometry Course 3, Lesson 5-6