1-4 The Pythagorean Theorem. Video Tutor Help Find a side Brain Pop The Pythagorean Theorem Using the Pythagorean Theorem to find the hypotenuseUsing.

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1-4 The Pythagorean Theorem

Video Tutor Help Find a side Brain Pop The Pythagorean Theorem Using the Pythagorean Theorem to find the hypotenuseUsing the Pythagorean Theorem to find the hypotenuse (1-4) The Pythagorean Theorem Khan Academy

Video Tutor Help Using the Pythagorean Theorem to find the hypotenuse

Worksheets 1-4 Note-Taking Guide 1-4 Practice 1-4 Guided Problem Solving

Vocabulary Practice Chapter 1 Vocabulary (Electronic) Flash Cards

Additional Lesson Examples 1-4 Step-by-Step Examples

Lesson Readiness 1-4 Problem of the Day 1-4 Lesson Quiz

Find the length of the hypotenuse of a right triangle whose legs are 6 ft and 8 ft. The Pythagorean Theorem LESSON 1-4 The length of the hypotenuse is 10 ft. a 2 + b 2 = c 2 Use the Pythagorean Theorem = c 2 Substitute a = 6, b = = c 2 Simplify. 100 = c 2 Add. 100 = c 2 Find the positive square root of each side. 10 = cSimplify. Additional Examples

Example 4-1a KITES Find the length of the kite string. The kite string forms the hypotenuse of a right triangle. The vertical and horizontal distances form the legs. Find the Length of the Hypotenuse

Example 4-1a Answer: The kite string is 13 feet long. The equation has two solutions, 13 and –13. However, the length of the kite string must be positive. Pythagorean Theorem Replace a with 5 and b with 12. Evaluate Add 25 and 144. Take the square root of each side. Simplify.

Example 5-1a Find the length of the hypotenuse of the right triangle. Pythagorean Theorem Replace a with 21 and b with 20. Evaluate 21 2 and Add 441 and 400. Find the Length of the Hypotenuse

Example 5-1b Take the square root of each side. Answer:The length of the hypotenuse is 29 feet.

Example 5-1c Find the length of the hypotenuse of the right triangle. Answer:The length of the hypotenuse is 5 meters.

A wheelchair ramp that leads into an apartment building doorway is 5 feet above the ground. The horizontal distance from the entrance to the end of the ramp is 16 feet. What is the length in feet of the ramp? Round to the nearest foot. The Pythagorean Theorem LESSON 1-4 The length of the ramp is about 17 feet. a 2 + b 2 = c 2 Use the Pythagorean Theorem = c 2 Substitute 5 for a and 16 for b = c 2 Simplify. 281 = c 2 Add. 281 = c 2 Find the positive square root of each side = c Simplify. 17 feet  cRound to the nearest foot. Additional Examples

Example 4-2a The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. Pythagorean Theorem Replace c with 33 and b with 28. Evaluate Subtract 784 from each side. Simplify. Take the square root of each side. Use a calculator. Find the Length of a Leg

Example 4-2a Answer: The length of the other leg is about 17.5 centimeters.

Example 5-2a Find the length of the leg of the right triangle. Pythagorean Theorem Replace c with 11 and a with 8. Evaluate 11 2 and 8 2. Solve a Right Triangle

Example 5-2b Subtract 64 from each side. Simplify. Take the square root of each side. ENTER 2nd [] Answer:The length of the leg is about 7.5 meters.

Example 5-2c Find the length of the leg of the right triangle. Answer:The length of the leg is about 12.7 inches.

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