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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Hover on the links, then click Next button
Minute Maid Park
Aerial view of field on a farm
Click on a hyperlink to learn more about Pythagorean Theorem and triangles.
Hover on the links to read about the similarities between the diagrams.
Now, click on Triangle.
C 2 = A 2 + B 2
Question: Find the length of the hypotenuse of a right triangle,
if a = 12 and b = 5.
C 2 = 12 2 + 5 2
C 2 = 144 + 25
C 2 = 169
C = √169
C = ± 13
The length of the hypotenuse is 13 units.
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.
Question: Match the legs of a triangle with the parts of a sailboat.
A = mast
Click on Return or Previous button to view more real life problems.
Question: Look at the trapezoid below.
Find the missing leg.
Question: Find the length of the missing legs.
C 2 = 8 2 + 3 2
C 2 = 64 + 9
C = √ 73
The length of the hypotenuse is √ 73.
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.
C 2 = 9 2 + 12 2
C 2 = 81 + 144
C 2 = 225
√ C = √ 225
C = 15
The length of the hypotenuse is 15.
Question: Find leg b if leg a = 3 and c = 5.
Click on the Next button to find the answer.
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.
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.
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.
Question: Find the length of the missing side.
Let b = 5, and c = 15.
Click the Next button to see if you answered correctly.
15 2 = a 2 + 5 2
225 = a 2 + 25
√ 200 = √ a 2
14 = a
The length of Leg a is 14 units.
Find the missing leg
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
Question: Let a = 32 – 10, and b = 26.
Click on the Next button for answer.
= ( 32 - 10 ) 2 + 26 2
= 22 2 + 26 2
= 484 + 676
C = 34.06
The c side of the “field” is ~34.06 meters
Question: Which field is most likely an example of a quadrilateral?
Click on the Next button for the answer.
You must be able to visualize and manipulate
the legs of the triangle, and understand the
Pythagorean Theorem concept to solve this problem.