Pythagorean Theorem

Warm Up

Find the length of the segment.

Objective DOL

SWBAT solve and interpret problems with the Pythagorean Theorem

Given 2 CR problems, SW solve and interpret problems with the Pythagorean Theorem

Warm Up

EQ: How can shapes solve problems?

A Right Triangle

LegHypotenuse

Leg

(the long side)b

a

c

Pythagorean’s Theorem

Let’s See an Example!

106

a2 + b2 = c2

82 + 62 = 102

64 + 36 = 100100 = 100

8

Heating Up On Fire

Trying it Out

13

5

c8

6

10c

13.9

Heating Up

8

6

a2 + b2 = c2

82 + 62 = c2

64 + 36 = c2

100 = c2

c = 100

10c

c = 10

On Fire

13

5

a2 + b2 = c2

52 + 132 = c2

25 + 169 = c2

194 = c2

c = 194

13.9c

c = 13.9

Light shoe Dark shoe

Pair Trade – Do yours, then trade and check

11

6

c7

3

7.62c

12.53

What if we need a leg?

15x

9√𝑥2=√144𝑥=12

12

Long hair Short hair

Pairs Trade

3024

15x

2520

x18

Long Hair

√𝑥2=√225𝑥=15 15

x

2520

Short Hair

√𝑥2=324𝑥=18 18

x

3024

Speed Test

√𝟑𝟗

√𝟑

√𝟒𝟏

√𝟔

√𝟏𝟏𝟓

𝟑√𝟐𝟑

1 2

Steps to solving real world problems:

1) Draw a diagram of the scenario.

2) Label the parts you know.

3) Determine the missing information you’re looking for.

4) Use Pythagorean Theorem to solve.

Trucks and ladders

Your top fire truck has a 50 foot ladder. There’s a fire at Hotel Eleganté and you need to keep your truck 35 feet away from the building. What’s the tallest window you can reach?

Thievery

Its Friday night, so you’re planning to rob a castle. Your best escape plan is to zip line to safety. How long does your cable need to be?

Did you know?

The size of a television is measured by the length of its diagonal.

Use that information to help you answer the next question.

Apply it!

Mr. Mallett wants to buy a new 42 inch television. The height of the television is 29 inches. He has an entertainment center that will hold a TV 28 inches wide. Will the new 42 inch TV fit?

No, the TV is 30.4 inches wide

42 inches

29 in

ches

x inches

Remember this?

Sketch the situation

To miss an ice floe, a boat travels 9 miles south and 12 miles east from its original spot.

How far out of their way did they travel?

9 miles

12 miles

x

92 + 122 = c2

225= c2

c = 15 milesThey travelled 21 miles (9 + 12)

6 miles out of the way

Let’s add a challenge: 2 Triangles!

Suppose a roller coaster vertically climbs 200 feet higher than its starting point making a horizontal advance of 350 feet. When it comes down, it will make a horizontal advance of 45 feet.

Sketch the situation.

200 ft

350 ft 45 ft

Use the Pythagorean Theorem to solve.

1) How far will the roller coaster travel to the top of the ride?

403. 1 feet

2) How far will the roller coaster travel on the downhill track?

205 feet

200 ft

350 ft 45 ft

x ft x ft

Summarize

How can shapes solve problems?

DOL Part 1

Carlos wants to buy a new 50-inch flat screen television and mount it on his wall. He knows the TV is 38 inches wide. He wants there to be 4 feet from the ground to the bottom of his TV, and he wants to hang a shelf 1 foot above the top of the TV for the cable box. How high on the wall will the shelf be hanging?

Sketch the situation (2 pts)Find the height of the TV (2 pts)Find how high he should hang the shelf (1pt)

1 ft

50 inches

38 inches

32.5 inches

4 feet

92.5 inchesor7.71 feet

DOL Part 2

When you turn off Platte onto Nevada you have to drive an extra 12 feet north and 14 feet east to get around the William Jackson Palmer Statue. If that statue wasn’t there, what would be the distance you would drive to make that turn? How far out of the way to you go to get around the statue?

Sketch the situation (2 pts)Find the distance of the turn w/o statue(2 pts)Distance out of the way (1pt)

12 feet

14 feet

18.4 feet

7.6 feet out of the way