4-8 The Pythagorean Theorem

0806.4.1 Use and apply the Pythagorean Theorem to solve contextual problems

The Pythagorean Theorem

4-8 The Pythagorean Theorem

Warm UpUse a calculator to find each value. Round to the nearest hundredth.

1.

2.

3.

4.

5.48

3.74

7.42

6.93

4-8 The Pythagorean Theorem

What is a formula? When would you use a formula outside of

school? Carpenter- Building a house Pharmacist- Measuring out liquid medicine Other examples?

4-8 The Pythagorean Theorem

Pythagoras was born on the Aegean island of Samos. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.

4-8 The Pythagorean Theorem

On Your Paper, I would like for you to write what you remember from 7th grade about the Pythagorean Theorem…any ideas?

After watching the video, any other ideas about the Pythagorean Theorem?

http://www.youtube.com/watch?v=DRRVu-RHQWE&feature=related

4-8 The Pythagorean Theorem

When I say right triangle, what does that mean? Pythagoras determined that if you know 2 sides of a right triangle, you can determine the other side

4-8 The Pythagorean Theorem

4

5

c

6.40 c

Pythagorean TheoremSubstitute for a and b.

a2 + b2 = c2

42 + 52 = c2

16 + 25 = c2

41 = c

Simplify powers. Solve for c; c = c2.

Additional Example 1A: Finding the Length of a Hypotenuse

Find the length of the hypotenuse to the nearest hundredth.

41 = c2

4-8 The Pythagorean Theorem

triangle with coordinates (–2, –2), (–2, 4), and (3, –2)

x

y

The points form a right triangle.

(–2, –2)

(–2, 4)

(3, –2)

Check It Out: Example 1B

7.81 c

Pythagorean Theorema2 + b2 = c2

62 + 52 = c2

36 + 25 = c2

61 = cSimplify powers. Solve for c; c = c2.

Substitute for a and b.

Find the length of the hypotenuse to the nearest hundredth.

4-8 The Pythagorean Theorem

Additional Example 2: Finding the Length of a Leg in a Right Triangle

25

7

b

Find the positive square root.

b = 24

a2 + b2 = c2

72 + b2 = 252

49 + b2 = 625–49 –49

b2 = 576

Solve for the unknown side in the right triangle to the nearest tenth.

Pythagorean TheoremSubstitute for a and c. Simplify powers. Subtract 49 from each side.

4-8 The Pythagorean Theorem

1st step- draw your other 2 lines- that will give you a and b!a2 + b2 = c2

42 + 72 = c2

16 + 49 = c2

65= c2

8.1= c

4-8 The Pythagorean Theorem

1st step- draw your other 2 lines- that will give you a and b!a2 + b2 = c2

32 + 82 = c2

65 = c2

8.5 = c

4-8 The Pythagorean Theorem

a2 + b2 = c2

3502 + 7252 = c2

122,500 + 525,625 = c2

648,125 = c2

805 ≈ c Find the positive square root.

Substitute for a and b.Pythagorean Theorem

The two planes are approximately 805 miles apart.

Two airplanes leave the same airport at the same time. The first plane flies to a landing strip 350 miles south, while the other plane flies to an airport 725 miles west. How far apart are the two planes after they land?

Simplify powers.

Add.

4-8 The Pythagorean Theorem

a2 + b2 = c2

902 + 902 = c2

8100 + 8100 =c2

16200 = c2

127.3 ≈ c

4-8 The Pythagorean Theorem

a2 + b2 = c2

252 + 102 = c2

625 + 100 =c2

725 = c2

26.9 ≈ c Find the positive square root.

Substitute for a and b.Pythagorean Theorem

You have locked yourself out of the house and the only open window is one the 2nd floor, 25 feet above the ground. Because there is a bush by the window, you must place the ladder 10 feet away from the house. What length of ladder do you need?

Simplify powers.

Add.

4-8 The Pythagorean Theorem

Oscar’s dog house is shaped like a tent. The slanted sides are both 5 ft. long and the bottom of the house is 6 ft across. What is the height of his dog house, at its tallest point.

4-8 The Pythagorean Theorem

1. Identify the height of the triangle.

A. 14 m

B. 15 m

C. 16 m

D. 17 m

Lesson Quiz for Student Response Systems

4-8 The Pythagorean Theorem

2. Identify the length of side c to the nearest meter.

A. 9 m

B. 10 m

C. 11 m

D. 12 m

Lesson Quiz for Student Response Systems