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W-up 1/19 Find the missing value – show all work x 60 x x x 4 8 x

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Applications of the Pythagorean Theorem Section 9.4

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Problem Solving Strategy Draw a diagram to help with difficult problems. Label what you know and use a variable for what you do not know. Use the Pythagorean Theorem to find the missing lengths. a 2 + b 2 = c 2

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Example 1 Find the area of a rectangular rug if the width is 12 feet and the diagonal measures 20 feet. Step 1: Draw a picture Step 2: Label what you know Step 3: Use a² + b² = c² to solve for the missing side Now find area: 12 feet 20 feet x 16 ft.

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Example 2 A 20 ft ladder reaches a window 16 ft high. How far is the foot of the ladder from the base of the building? How far must the foot of the ladder be moved to lower the top of the ladder by 2 ft? 16 ft 20 ft x n To find how far the ladder will be moved you find the difference between x and n x=12 ft. ? 14

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Example 3 Susan wants to mail her nephew a Christmas gift. She has picked out a bat that is 27 inches long. The only box available is 15-by-20-by-12- inches. Will the bat fit in the box? 15 in. 12 in. 20 in. The bat cannot fit lying straight along one side, but where is the longest measurement? What do we need in order to find that measurement? b x

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Example 3 continued… Use x to find b first solve for x 25 in. 15 in. 12 in. 20 in. b x Yes, the bat will fit on the longest diagonal. If the bat is 27 in =729 We need 729 and we have 769. It will ship!

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Ex. 4 Algebra and Pythagorean C A D B Find the value of x and the lengths of sides AB, BC, CD of triangle ABC when given the following: AD=32, CD= 4x, DB = 3x, AC = 40 Insert what we know: 40 4x 32 3x Use Pythagorean theorem on two separate triangles! Substitute 6 in for x and find the indicated lengths. AB = 50, CD =24, BC = 30

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Summary To solve a word problem… Homework: WS 9.4

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