Transcript Document 7120089

11.7 and 11.8 Pythagorean Thm.
PYTHAGOREAN THEOREM
The Pythagorean Theorem is one of the
most famous theorems in mathematics.
The relationship it describes has been
known for thousands of years.
THEOREM
Pythagorean Theorem
In a right triangle, the
square of the length of
the hypotenuse is
equal to the sum of
the squares of the
lengths of the legs.
2
2
c =a +b
2
c
a
b
Finding the Length of a Hypotenuse
12
Find the length of the hypotenuse of the right
5
triangle. Tell whether the side lengths form a
x
SOLUTION
Pythagorean triple.
2
2
2 Pythagorean Theorem
(hypotenuse) = (leg) + (leg)
x 2 = 5 2 + 12 2
Substitute
x 2 = 25 + 144
Multiply.
x 2 = 169
Add.
x = 13
Find the positive square root.
Because the side lengths 5, 12, and 13 are
integers, they form a Pythagorean triple.
Finding the Length of a Leg
Find the length
of the
legtriangles
of the right
triangle.
Many
right
have
side lengths7 that
do not form a Pythagorean triple.
SOLUTION
x
14
(hypotenuse)2 = (leg)2 + (leg)2
2
2
2
14 = 7 + x
2
196 = 49 + x
147 = x 2
147 = x
49 • 3 = x
7 3 =x
Pythagorean Theorem
Substitute.
Multiply.
Subtract 49 from each side.
Find the positive square root.
Use product property.
Simplify the radical.
75 m
5 3 m
w  13  9
2
2
2
w  169  81
w  15.8 m
w
76.5 ft.
d  8100  8100
2
d  16,200
d  127.3'
Assignment
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