Pythagorean Theorem

Warm Up

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 Leg Hypotenuse Leg

Pythagorean’s Theorem

Let’s See an Example! 10 6 a 2 + b 2 = c = = = 100 8

Heating Up On Fire Trying it Out 13 5 c c 13.9

Heating Up 8 6 a 2 + b 2 = c = c = c = c 2 c =  c c = 10

On Fire 13 5 a 2 + b 2 = c = c = c = c 2 c =  c c = 13.9

Light shoe Dark shoe Pair Trade – Do yours, then trade and check 11 6 c c 12.53

What if we need a leg? 15 x 9 12

Long hair Short hair Pairs Trade x x 18

Long Hair 15 x 25 20

Short Hair 18 x 30 24

Speed Test 12

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?

Construction Tip To build a house, you need lots of right angles. It’s hard to use a protractor or T-Square to measure perfect angles when the sides can be more than 10 feet long. Instead of measuring out the angles, you can use triangles.

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 inches 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 = c 2 225= c 2 c = 15 miles They 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 ft45 ft

Use the Pythagorean Theorem to solve. 1) How far will the roller coaster travel to the top of the ride? feet 2) How far will the roller coaster travel on the downhill track? 205 feet 200 ft 350 ft45 ft x ft

Pythagorean Theorem Word Problems 8 Pythagorean Theorem problems will be passed out to you and your partner. Work with your partner to solve. Remember you must draw a diagram for each one! Take turns writing. You will turn in one paper between the two of you when you’re done.

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 inches or 7.71 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