W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

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W-up 1/19 Find the missing value – show all work 3. 9 3 5 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 6 2 x

Transcript of W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

Page 1: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

W-up 1/19

Find the missing value – show all work

3.

9

3511

x 60

x

2.1.

4.

12

5.

30

x

x4

8

62

x

Page 2: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

Applications of the Pythagorean Theorem

Section 9.4

Page 3: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

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

Page 4: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

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 feetx

2 2 2

2

2

12 20

144 400

144 144

256

16

x

x

x

x ft

16 ft.

12 16

192 .

A lw

A

A ft

Page 5: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

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 ft20 ft

x nTo find how far the ladder will be moved you find the difference between x and n

x=12 ft.

?

144

400256

2016

2

2

222

x

x

x

512

204

400196

2014

2

2

222

n

n

n

n

14

2 51 12

Page 6: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

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

Page 7: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

Example 3 continued…

Use x to find b

first solve for x2 2 2

2

2

15 20

225 400

625

25 .

x

x

x

x in

25 in.

15 in.

12 in.

20 in.

b

x

2 2 2

2

2

12 25

144 625

769

769

b

b

b

b in

Yes, the bat will fit on the longest diagonal.

If the bat is 27 in. 272=729

We need 729 and we have 769. It will ship!

Page 8: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

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!

2 2 232 (4 ) 40x 2

2

1024 16 1600

16 576

x

x

2

2

16 576

36

6

x

x

x

Substitute 6 in for x and find the indicated lengths.

AB = 50, CD =24, BC = 30

Page 9: W-up 1/19 Find the missing value – show all work 3. 9 11 x 60 x 2. 1. 4. 12 5. 30 x x 4 8 x.

Summary

To solve a word problem…

Homework: WS 9.4