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.
a
c
b
LEGS
a² + b² = c²
HYPOTENUSE
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.)
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.
2nd
3rd
1st
BASE
a² + b² = c²
(90)² + (90)²= c²
8100 + 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 Math
Television 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?
12
inches
?
15 inches
The Equation
a² + b² = c²
(12)² + (15)² = c²
144 + 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.
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
8 miles
?
Pretty Street
7 Miles
The Equation
a² + b² = c²
(8)² + (7)² = c²
64 + 49 = c²
113 = c²
(√113) = (√c²)
10.6 = c
24 miles
10
miles
?
The Equation
a² + b² = c²
(10)² + (24)² = c²
100 + 576 = c²
676 = c²
(√676) = (√c²)
26 = c
Land Ho
How far is the sailboat
from the lighthouse, to
the nearest kilometer?
(on the next slide)
130 km
50 km
?
The Equation
a² + b² = c²
(50)² + (130)² = c²
2500 + 16900 = c²
19400 = c²
(√19400) = (√c²)
139 = c