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Example 3-5b Objective Find length using the Pythagorean Theorem

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Example 3-5b Vocabulary Leg Either of the two sides that form the right angle of a right triangle legs

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Example 3-5b Vocabulary Hypotenuse The side opposite the right angle in a right triangle Hypotenuse

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Example 3-5b Vocabulary Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs C 2 = A 2 + B 2 Hypotenuse Legs

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Example 3-5b Vocabulary Right triangle A triangle with exactly one angle that measures 90 0

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Lesson 3 Contents Example 1Find the Length of the Hypotenuse Example 2Find the Length of a Leg Example 3Solve a Real-Life Problem Example 4Identify Right Triangles Example 5Identify Right Triangles

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Example 3-1a GYMNASTICS A gymnastics tumbling floor is in the shape of a square with sides 12 meters long. If a gymnast flips from one corner to the opposite corner, about how far has he flipped? Draw the picture Draw the right angle Remember: The legs come off the right angle The hypotenuse is the diagonal (the longest side)

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Example 3-1b To solve, find the length of the hypotenuse c. Write Pythagorean Theorem Replace a with 12 Evaluate Add. and b with 12. 1/5

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Example 3-1b Do the inverse on both sides of the equal sign Answer: Ask what is being done to the variable The variable is being squared cc = 16.97 1/5 The inverse of squaring is the square root Find the square root of c 2 (c c = c 2 ) Find the square root of 288 Add dimensional analysis c = 16.97

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Example 3-1b Answer: c = 16.97 1/5 Add dimensional analysis meters

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Example 3-1c SEWING Rose has a rectangular piece of fabric measuring 28 inches in length and 16 inches in width. She wants to decorate the fabric with a piece of lace sewn across both diagonals. How much lace will Rose need to complete the project? Answer: c = 64.50 inches Draw picture and label dimensions before solving 1/5

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Example 3-2a Find the missing measure of the triangle below. Write the Pythagorean Theorem Replace b with 9 Replace c with 15. 2/5

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Example 3-2b Do the inverse on both sides of the equal sign Ask “what is being done to the variable?” The variable is being added by 81 2/5 Find 15 2 255 = Find 9 2 a 2 + 81

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Example 3-2b 2/5 Bring down 255 255 =a 2 + 81 255 Subtract 81 - 81 Bring down = a 2 + 81 = a 2 + 81 Subtract 81 - 81 Combine “like” terms 144 Bring down = a 2 = a 2 Combine “like” terms + 0

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Example 3-2b 2/5 Use the Identity Property to add a 2 + 0 255 =a 2 + 81 255- 81 = a 2 + 81- 81 144= a 2 + 0 144 = a 2 Ask “what is being done to the variable?” The variable is being squared Do the inverse on both sides of the equal sign Find the square root of both sides of the equal sign

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Example 3-2b 2/5 Find the square root of 144 255 =a 2 + 81 255- 81 = a 2 + 81- 81 144= a 2 + 0 144 = a 2 12 = Find the square root of a 2 a Add dimensional analysis cm Answer:

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Example 3-2c Find the missing measure of the triangle below. Round to the nearest hundredth if necessary. Answer: a = 18.73 in. Draw the picture before solving 2/5

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Example 3-3a TELEVISION Televisions are measured according to their diagonal measure. If the diagonal of a television is 36 inches, and its height is 21.6 inches, what is its width? 3/5 Draw the picture before solving Include the dimensions of each leg and the diagonal

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Example 3-3b Write the Pythagorean Theorem 3/5 Since c is the diagonal replace c with 36

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Example 3-3b A is the height of the TV so replace a with 21.6 3/5 B is the width of the TV so define your variable as b

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Example 3-3b 3/5 Find 36 2 1,296 = Find 21.6 2 466.56 Bring down + b 2 + b 2 Ask “what is being done to the variable?” The variable is being added by 466.56 Do the inverse on both sides of the equal sign

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Example 3-3b 3/5 Bring down 1,296 1,296 =466.56+ b 2 1,296 Subtract 466.56 - 466.56 Bring down = 466.56 = 466.56 Subtract 466.56 - 466.56 Bring down + b 2 + b 2

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Example 3-3b 3/5 Combine “like” terms 1,296 =466.56+ b 2 1,296 - 466.56 = 466.56- 466.56+ b 2 829.44 Bring down = = Combine “like” terms 0 + b 2 Use the Identity Property to add 0 + b 2 829.44 = b 2 Ask “what is being done to the variable?” The variable is being squared Find the square root of both sides of the equal sign

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Example 3-3b 3/5 1,296 =466.56+ b 2 1,296 - 466.56 = 466.56- 466.56+ b 2 829.44=0 + b 2 829.44 = b 2 Find the square root of 829.44 Find the square root of b 2 28.80= b Add dimensional analysi In. Answer:

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Example 3-3c SWIMMING The diagonal of a rectangular swimming pool measures 60 feet. Find the length of the pool if the width measures 30 feet. Round to the nearest hundredth if necessary. Answer: b = 51.96 ft 3/5

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Example 3-4a Determine whether a triangle with the lengths 2.5 centimeters, 6 centimeters, and 6.5 centimeters is a right triangle. Write the Pythagorean Theorem Remember c is the longest side so replace c with 6.5 A is the shortest side so replace a with 2.5 4/5 6.5 2 = 2.5 2 + B is the remaining leg so replace b with 6 6 2

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Example 3-4a Determine whether a triangle with the lengths 2.5 centimeters, 6 centimeters, and 6.5 centimeters is a right triangle. 4/5 6.5 2 = 2.5 2 + 6 2 Find 6.5 2 42.25 Find 2.5 2 = 6.25 Find 6 2 + 36 Combine “like” terms 42.25 = 42.25 Both sides of the equal sign have the same value If both are equal, then the triangle is a right triangle Answer: The triangle is a right triangle.

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Example 3-4b Determine whether a triangle with the lengths 5 inches, 12 inches, and 13 inches is a right triangle. Answer: the triangle is a right triangle 4/5

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Example 3-5a Determine whether a triangle with the lengths 5 feet, 6 feet, and 8 feet is a right triangle. 5/5 Write the Pythagorean Theorem Remember c is the longest side so replace c with 8 8 2 = A is the shortest side so replace a with 5 5 2 + B is the remaining leg so replace b with 6 6262

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Example 3-5a Determine whether a triangle with the lengths 5 feet, 6 feet, and 8 feet is a right triangle. 5/5 8 2 =5 2 +6262 Find 8 2 64 = Find 5 2 25 + Find 6 2 36 Combine “like” terms 64 = 61 Both sides of the equal sign do not have the same value Since both sides are not equal, it cannot be a right triangle Answer: It is not a right triangle

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Example 3-5b Determine whether a triangle with the lengths 4.5 centimeters, 9 centimeters, and 12.5 centimeters is a right triangle. Answer: It is not a right triangle 5/5

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End of Lesson 3 Lesson 11:3The Pythagorean Theorem9 - 21 All Assignment

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