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Geometry : The Pythagorean Theorem. Pythagorean Theorem. A formula named after the Greek mathematician Pythagoras is used. right triangle. Hover on the links, then click Next button. Attic of house. Houston Astros’ Minute Maid Park. Sailboat. Kite Flying. Aerial view of field on a farm.

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pythagorean theorem
Pythagorean Theorem
  • A formula named after the Greek mathematician Pythagoras is used.
  • right triangle

Hover on the links, then click Next button

slide3

Attic of house

Houston Astros’

Minute Maid Park

Sailboat

Kite Flying

Aerial view of field on a farm

Click on a hyperlink to learn more about Pythagorean Theorem and triangles.

about triangles and sailboats
About Triangles and Sailboats

Sailboat

Triangle

Hover on the links to read about the similarities between the diagrams.

Now, click on Triangle.

example 1
Example 1

C 2 = A 2 + B 2

Question: Find the length of the hypotenuse of a right triangle,

if a = 12 and b = 5.

slide6

Answer: C 2 = A 2 + B 2

C 2 = 12 2 + 5 2

C 2 = 144 + 25

C 2 = 169

C = √169

C = ± 13

C

5

12

The length of the hypotenuse is 13 units.

know your sailboats the real world
Know Your Sailboats the Real World

Use of the wind is one of the oldest forms of powering a vessel. Sailboats range in size and complexity, but all have basically the same four components.

  • The hullcarries the passengers and supports the rigging.
  • The rigging includes many parts of the sailboat, such as the lines (sheetsand halyards), mainsail, headsail (jib), boom, and mast.
  • The keel or centerboard is attached to the bottom of the hull and keeps the boat from sliding sideways through the water.
  • The rudderis used to steer the sailboat, turned by a tiller or steering wheel.

Question: Match the legs of a triangle with the parts of a sailboat.

slide8

Answer: B = boom

A = mast

Click on Return or Previous button to view more real life problems.

trapezoid example
Trapezoid Example

Question: Look at the trapezoid below.

Find the missing leg.

Question: Find the length of the missing legs.

slide10

Answer: C 2 = A 2 + B 2

C 2 = 8 2 + 3 2

C 2 = 64 + 9

C = √ 73

The length of the hypotenuse is √ 73.

real world attic without proper insulation
Real World Attic without ProperInsulation

Question: Find and then label the triangle.

Next, if a = 9 and b = 12, find the missing leg.

Click the Next button to see if you got the correct answer.

slide12

Answer: C 2 = A 2 + B 2

C 2 = 9 2 + 12 2

C 2 = 81 + 144

C 2 = 225

√ C = √ 225

C = 15

The length of the hypotenuse is 15.

diamond triangle example
Diamond - Triangle Example

Question: Find leg b if leg a = 3 and c = 5.

Click on the Next button to find the answer.

slide14

Answer: C 2 = A 2 + B 2

5 2 = 3 2 + B 2

25 = 9 + B 2

25 - 9 = B 2

√ 16 = √ B 2

4 = B

The length of Leg B is 4 units.

houston astro s baseball diamond
Houston Astro’s Baseball Diamond

Question: A baseball scout uses many different test to determine whether or not to draft a particular player. One test is how quickly he can throw the ball from home plate to second base. On a baseball diamond, the distance from one base to the next is 90 feet. What is the distance from home plate to second base?

Click the Next button to see the answer.

slide16

Answer: C 2 = A 2 + B 2

C 2 = 90 2 + 90 2

C 2 = 8100 + 8100

√ C 2 = √16200

C = 127.28 feet

There is a distance of ~127 feet from the home plate

to second base on a baseball diamond.

slide17

Isosceles Triangle Example

Question: Find the length of the missing side.

Let b = 5, and c = 15.

Click the Next button to see if you answered correctly.

slide18

Answer: C 2 = A 2 + B 2

15 2 = a 2 + 5 2

225 = a 2 + 25

√ 200 = √ a 2

14 = a

The length of Leg a is 14 units.

slide19

Real World Isosceles Triangle

Find the missing leg

slide20

Instructions in drawing Poom Khao Bin Design

1. Draw a square like a kite. Please see the shape, size and other detail in the example.2. When the outline is completed, draw two inner pictures shape like two drops of water. The smaller one must have lighten colour than the outer one.3. Draw the outline of the outer petals lightly.4. Draw the outer petals in details. All petals must be stuck with the outer "drop of water". Begin with the left and the right petals. The instructions in drawing the four petals are similar to those of Krajang Ta Oil. The difference is that in this case, we draw only half of the design.

Sometimes the real beauty of math is in the design. Enjoy this piece of jewelry or design.

Answer: c 2 = a 2 + b 2

= 2 2 + .7 2

= 4 + .49

C = √4.49

quadrilateral triangle example
Quadrilateral Triangle Example

32

26

10

Question: Let a = 32 – 10, and b = 26.

Find c.

Click on the Next button for answer.

slide22

Answer: c 2 = a 2 + b 2

= ( 32 - 10 ) 2 + 26 2

= 22 2 + 26 2

= 484 + 676

= 1160

C = 34.06

The c side of the “field” is ~34.06 meters

real world example of a quadrilateral a farm field
Real World Example of a Quadrilateral- a Farm Field

Question: Which field is most likely an example of a quadrilateral?

Click on the Next button for the answer.

slide24

Answer: Field 2 is shaped most like a quadrilateral.

You must be able to visualize and manipulate

the legs of the triangle, and understand the

Pythagorean Theorem concept to solve this problem.

slide25
Teks
  • §111.36. Mathematical Models with Applications
  • c) Knowledge and skills.
  • The student uses a variety of strategies and approaches to solve both routine and non-routine problems. The student is expected to: (A) compare and analyze various methods for solving a real-life problem;
  • (B) use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; and
  • (C) select a method to solve a problem, defend the method, and justify the reasonableness of