Presentation on theme: "W-up 1/19 Find the missing value – show all work x 60 x"— Presentation transcript:
1 W-up 1/19 Find the missing value – show all work 3. 2. 1. 11 12 x 60 x 85.44.30xx
2 Applications of the Pythagorean Theorem Section 9.4
3 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.a2 + b2= c2
4 Example 1Find the area of a rectangular rug if the width is 12 feet and the diagonal measures 20 feet.Step 1: Draw a pictureStep 2: Label what you knowStep 3: Use a² + b² = c² to solvefor the missing sideNow find area:12 feet20 feetx16 ft.
5 Example 2A 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 ft20 ftxn14x=12 ft.To find how far the ladder will be moved you find the difference between x and n?
6 Example 3Susan 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?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?b15 in.12 in.20 in.x
7 Yes, the bat will fit on the longest diagonal. Example 3 continued…Use x to find bfirst solve for x15 in.12 in.20 in.bxYes, the bat will fit on the longest diagonal.25 in.If the bat is 27 in. 272=729We need 729 and we have 769. It will ship!
8 Ex. 4 Algebra and Pythagorean 404xxCA D BFind 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 = 40Insert what we know:Use Pythagorean theorem on two separate triangles!Substitute 6 in for x and find the indicated lengths.AB = 50, CD =24, BC = 30