4-8 the pythagorean theorem 0806.4.1 use and apply the pythagorean theorem to solve contextual...
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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