1-5 Using the Pythagorean Theorem

Video Tutor Help Find a side Brain Pop The Pythagorean Theorem Using the Pythagorean Theorem to find the legUsing the Pythagorean Theorem to find the leg (1-5) Using the Pythagorean Theorem Khan Academy

Video Tutor Help Using the Pythagorean Theorem to find the leg

Worksheets 1-5 Note-Taking Guide 1-5 Practice 1-5 Guided Problem Solving

Vocabulary Practice Chapter 1 Vocabulary (Electronic) Flash Cards

Additional Lesson Examples 1-5 Step-by-Step Examples

Lesson Readiness 1-5 Problem of the Day 1-5 Lesson Quiz

The Pythagorean Theorem LESSON in. 19 cm 31 ft 7 in. 1. Find the hypotenuse of a right triangle with legs of 9 in. Round to the nearest inch. 2. A right triangle has legs of 5 cm and 18 cm. What is the length of its hypotenuse to the nearest centimeter? 3. A staircase is 20 ft high. The horizontal distance from one end of the staircase to the other end is 24 ft. What is the distance from the top of the staircase to the bottom of the staircase? Round to the nearest foot. 4. A book is leaning with one end at the top edge of a bookend. The bookend is 6 in. high. The distance along the shelf from the edge of the book to the bottom of the bookend is 4 in. How long is the book? Round to the nearest inch. Lesson Quiz

Find the missing leg length of the triangle. Using the Pythagorean Theorem LESSON 1-5 The length of the other leg is 5 cm. a 2 + b 2 = c 2 Use the Pythagorean Theorem. a = 13 2 Substitute 12 for b and 13 for c. a = 169 Simplify. a 2 = 25Subtract. a = 5Simplify. a 2 = 25Find the positive square root of each side. Additional Examples

The bottom of a 10-foot ladder is 2.5 ft from the side of a wall. How far, to the nearest tenth, is the top of the ladder from the ground? Using the Pythagorean Theorem LESSON 1-5 The diagram shows a right triangle with hypotenuse 10 ft and leg 2.5 ft. The distance from the top of the ladder to the ground is a. Additional Examples

(continued) Using the Pythagorean Theorem LESSON 1-5 The distance from the top of the ladder to the ground is about 9.7 ft. a 2 + b 2 = c 2 Use the Pythagorean Theorem. a 2 + (2.5) 2 = 10 2 Substitute b = 2.5 and c = 10. a = 100Multiply. a 2 = 93.75Subtract 6.25 from each side Use a calculator. a = 93.75Find the positive square root. a 9.7Round to the nearest tenth. Additional Examples

Example 5-1a RAMPS A ramp to the entrance of a newly constructed building must be built according to accessibility guidelines stated in the Americans with Disabilities Act. If the ramp is 24.1 feet long and the top of the ramp is 2 feet off the ground, how far is the end of the ramp from the entrance? Notice the problem involves a right triangle. Use the Pythagorean Theorem.

The square of equals the sum of the the hypotenuse squares of the legs. Words Simplify. Variables = Write the equation. Evaluate Subtract 4 from each side. Equation =

Example 5-1a Take the square root of each side. Simplify. Answer: The end of the ramp is about 24 feet from the entrance. Use the Pythagorean Theorem

Example 5-1b RAMPS If a truck ramp is 32 feet long and the top of the ramp is 10 feet off the ground, how far is the end of the ramp from the truck? Answer: about 30.4 ft

Example 5-3a Multiple-Choice Test Item A building is 10 feet tall. A ladder is positioned against the building so that the base of the ladder is 3 feet from the building. How long is the ladder? A 12.4 feetB 10.4 feet C 10.0 feetD 14.9 feet Read the Test Item Make a drawing to illustrate the problem. The ladder, ground, and side of the house form a right triangle. Use the Pythagorean Theorem

Example 5-3b Solve the Test Item Use the Pythagorean Theorem to find the length of the ladder. Pythagorean Theorem Replace a with 3 and b with 10. Evaluate 3 2 and Simplify.

Example 5-3c Take the square root of each side. Round to the nearest tenth. The ladder is about 10.4 feet tall. Answer:The answer is B.

Example 5-3d Multiple-Choice Test Item An 18-foot ladder is placed against a building which is 14 feet tall. About how far is the base of the ladder from the building? A 11.6 feetB 10.9 feet C 11.3 feetD 11.1 feet Answer:The answer is C.

Example 5-4a The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 48 ft, 60 ft, 78 ft The triangle is not a right triangle. Answer:no Pythagorean Theorem Replace a with 48, b with 60, and c with 78. Evaluate. Simplify. Indentify a Right Triangle

Example 5-4b The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 24 cm, 70 cm, 74 cm The triangle is a right triangle. Answer:yes Pythagorean Theorem Replace a with 24, b with 70, and c with 74. Evaluate. Simplify. Indentify a Right Triangle