Example 1: Solve a Right Triangle Example 2: Real-World Example

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Example 1: Solve a Right Triangle Example 2: Real-World Example Main Idea Example 1: Solve a Right Triangle Example 2: Real-World Example Lesson Menu

Solve problems using the Pythagorean Theorem. Main Idea/Vocabulary

a2 + b2 = c2 Pythagorean Theorem Solve a Right Triangle RAMPS A boat ramp has a base that is 25 feet long and 4.2 feet high. Write an equation that can be used to find the length of the ramp. Then solve. Round to the nearest tenth. a2 + b2 = c2 Pythagorean Theorem 4.22 + 252 = c2 Replace a with 4.2 and b with 25. Example 1

Definition of square root ± 25.4  c Use a calculator. Solve a Right Triangle 17.64 + 625 = c2 Evaluate 4.22 and 252. 642.64 = c2 Add 17.64 and 625. Definition of square root ± 25.4  c Use a calculator. Answer: Since length cannot be negative, the boat ramp is about 25.4 feet long. Example 1

STAIRS The stairs leading up to a commuter plane has a base that is 16 feet long and 7.5 feet high. Write an equation that can be used to find the length of the stairs. Then solve. Round to the nearest tenth. A. 16 – 7.5 = x; 8.5 feet B. 162 – 7.52 = x2; 14.1 feet C. 162 + 7.52 = x2; 17.7 feet D. 162 + 7.52 = x; 23.5 feet Example 1 CYP

CAMPING The cross section of a camping tent is shown below CAMPING The cross section of a camping tent is shown below. Find the width of the base of the tent. Each half of the cross section forms a right triangle. Use the Pythagorean Theorem. x Example 2

a2 + b2 = c2 Pythagorean Theorem 82 + x2 = 102 Replace a with 4.8 and c with 10. 64 + x2 = 100 Evaluate 82 and 102. 64 – 64 + x2 = 100 – 64 Subtract 64 from each side. x2 = 36 Simplify. Definition of square root x = 6 or –6 Simplify. Answer: The width of the base of the tent is x + x or 6 + 6 = 12 feet. Example 2

DESIGN The design shown below is formed by two isosceles triangles DESIGN The design shown below is formed by two isosceles triangles. What is the perimeter of the design? Round to the nearest tenth if necessary A. 52.9 in. B. 81.9 in. C. 96.9 in. D. 105.9 in. Example 2 CYP