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 = c²

LEGS

HYPOTENUSEa

b

c

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 Equation

a² + b² = c²(90)² + (90)²= c²8100 + 8100 = c²

16,200 = c²(√16,200) = (√c²)

127 = c

The Final Answer

The 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 Problem

You 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 Equation

a² + 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?

Perfe

ct Stre

et

Pretty Street

7 Miles

8 miles

?

The Equation

a² + b² = c²(8)² + (7)² = c²64 + 49 = c²

113 = c²(√113) = (√c²)

10.6 = c

The Final Answer

Cinderella 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 Equation

a² + b² = c²(50)² + (130)² =

c²2500 + 16900 =

c²19400 = 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.jpg

Georgia HOLT Mathematics Course 3

Pythagoras