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38. Given:
n
ABC
with
sides of measure
a
,
b
, and
c
,where
c
2
5
a
2
1
b
2
Prove:
n
ABC
is a
right triangle.
Proof:
Draw
DE
##
on line
,
with measure equal to
a
.At
D
,draw line
m
'
DE
##
.Locate point
F
on
m
so that
DF
5
b
.Draw
F
w
E
w
and call its measure
x
.
Because
n
FED
is a right triangle,
a
2
1
b
2
5
x
2
.
But
a
2
1
b
2
5
c
2
, so
x
2
5
c
2
or
x
5
c
.Thus,
n
ABC
>
n
FED
by SSS. This means
/
C
>
/
DE
.
Therefore,
/
C
must be a right angle, making
n
ABC
a right triangle.
39. Given:
n
ABC
with right angle at
C
,
AB
5
d
Prove:
d
5
Ï
(
x
2
2
w
x
1
)
2
1
w
(
y
2
2
w
y
1
)
2
w
Proof:
40.
First, use the Pythagorean Theorem to find the
length of the ladder, represented by
y
.
12
2
1
16
2
5
¬
y
2
144
1
256
5
¬
y
2
400
5
¬
y
2
Ï
400
w
5
¬
y
20
5
¬
y
The ladder is 20 feet long.
(2
1
12)
2
1
x
2
5
¬
20
2
14
2
1
x
2
5
¬
20
2
196
1
x
2
5
¬
400
x
2
5
¬
204
x
5
¬
Ï
204
w
x
5
¬
2
Ï
51
w
x
<
¬
14.3
The ladder reaches about 14.3 feet up the side of
the house.
41.
Let
x
be the hypotenuse of the triangle with
height 26
1
12 or 38 and base
}
1
2
}
(9) or 4.5.
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus

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