The Pythagorean Theorem
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Transcript of The Pythagorean Theorem
The Pythagorean Theorem
Stacie Evans
What is the Pythagorean Theorem?The Pythagorean Theorem relates the side lengths of a right triangle.In any right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
a² + b² = c²LEGS
HYPOTENUSEa
bc
http://web.rollins.edu/~jsiry/PythagoreanTriTheorem.jpg
Use the Pythagorean Theorem
to solve the following problems.
BASEBALL MATH How far does
the second baseman have to throw the ball in order to get the runner out before he slides into the home plate? (Round to the nearest whole number.)
BASE
3rd
2nd
1st
In a baseball diamond, the distance between each of the three bases and home plate are 90 feet and all form right angles. Therefore, you can use the Pythagorean Theorem to solve the question.
The Equationa² + b² = c²
(90)² + (90)²= c²8100 + 8100 = c²
16,200 = c²(√16,200) = (√c²)
127 = c
The Final AnswerThe second baseman would have to
throw the baseball 127 feet for the catcher to catch it before the runner
slides onto home plate.
Television MathTelevision sets are generally classified diagonally.
http://www.avland.co.uk/panasonic/tx32lxd500/tx32lxd500lrg.jpg
The ProblemYou want to purchase an entertainment center, but it holds only enough room in its cubicle for a 27 inch TV set. The length of your TV is 15 inches, and the height of your TV is 12 inches.The Question:
Will your TV fit into the cubicle?
15 inches
12inches
?
The Equationa² + b² = c²
(12)² + (15)² = c²144 + 225 = c²
369 = c²(√369) = (√c²)
19.2 = c
The Final Answer
The television is 19.2 inches. The television will fit into the 27 inch TV center.
The Miles from Where You Are
Cinderella and Prince Charming are meeting at the Palace on the corner of Perfect and Pretty Street. Cinderella is on Perfect Street and is 8 miles from the corner. Meanwhile, Prince Charming is on Pretty Street and is 7 miles from the corner. They are desperate to know how far away they are from each other. Can you find out how far apart they are?
Perfect Street
Pretty Street
7 Miles
8 miles
?
The Equationa² + b² = c²
(8)² + (7)² = c²64 + 49 = c²
113 = c²(√113) = (√c²)
10.6 = c
The Final AnswerCinderella and Prince Charming
are 10.6 miles apart.
The Helicopter FlightA helicopter flies 10 miles due north and then 24 miles due east. Then the helicopter flies in a straight line back to its starting point. What was the distance of the helicopter’s last leg back to its starting point?
10 miles
24 miles
?
The Equation a² + b² = c²
(10)² + (24)² = c²
100 + 576 = c²676 = c²
(√676) = (√c²)26 = c
The Final Answer
The distance of the helicopter’s last leg was 26 miles.
Land Ho How far is the sailboat
from the lighthouse, to the nearest kilometer? (on the next slide)
50 km
?
130 km
The Equationa² + b² = c²
(50)² + (130)² = c²
2500 + 16900 = c²
19400 = c²(√19400) = (√c²)
139 = c
The Final Answer• The sailboat is 139 kilometers
away from the lighthouse.
Bibliography
http://www.suite101.com/content/the-pythagorean-theorem-a21010http://www.disneylandpostcards.com/images/Cinderella.jpghttp://www.ltmparty.com/images/products/DU/large/5969.jpg http://www.wdwpublicaffairs.com/Resources/images/Cinderella_Castle_ice__36556655_500w.jpg http://neildthompson.com/wp-content/uploads/2010/08/MP900401198.jpg
http://www.stregisbalharbour.com/images/no-flash-views.jpg http://
www.cksinfo.com/clipart/traffic/boats/lighthouse-01.png http://
www.wpclipart.com/page_frames/school/certificate_frame.png http://
www.btinternet.com/~steve.sedgwick/images/Pythagguitar/pythagoras.jpgGeorgia HOLT
Mathematics Course 3Pythagoras