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1厅\ ' : °
Ų
th e h y p o te n u s e ? w
E x . 2 a ) W h a t v a r ia b ıe r e p r e s e n ts b ) I f p- 2 5 a n d r - 2 4 t h e n w -
.
P
th e h y p o te n u s e ?
E x . 1 a ) W h a t v a r ia b le re p re s e n ts r b ) If p- 8 a n d r - 1 5 t h e n w -
.
UU
is th e ! ņ ¢ (lo n g e s t s id e ) .
a s y o u k n o w th e o th e r h n s id e s . T h e p y th a g o re a n T h e o re m is. D y b
'= ć w h e re
1 .
In a X ' ' " th . ."
;?anyp s s i n g s i d ' ' " ' "
In tr o d u c tio n to P y th a g o re a n T h e o r e m
N a m e :.
P e rio d 1 1 / 1 0 / 2 0 0 8 G L
5 ) 6 , 9 , 6
只づ知卜
2 ) 6 , 8 , 10
吕
A ,
a
C
a n o b t u s e t r ia n g le .
If c z > a
z ◆ b
z. T h e n ö A ß C l s ıf c
z
< az
◆ bz
. T h e n ö A ß C l s
ın A A B C , c i s t h e ıe ng
t h o f t t n ıo ng
e s t s i d e .
o r e m s 5 - 7 - 2 [ p y t h a * o re a n ın * q u · ııt ı · s T h ·
V . P y th a g o r e a n I n e q u a litie s
O i T ( ;
Ł
E x p la in .
4 8a P y t h a g o r e a n t r ip ıe .
E x a m p ıe 3 0 ıd e n t ıfy ın g P y w h a g o r e a n T rıp ıe s
X * b ' . c
2is c a ııe d .
ÝR.
ył¢Y a ł, ł)
12A s e t o f t h r e e n o n z e r o w h o ıe n u m b e r s a , b ,
E x p ıa ın .
a P y t h a g o r e a n t r ıp ıe .
T e lı ıf t h e s id e ıe n g t h s f o r m
F in d t h e m ıs s ın g s ıd e ıe n g t h .
IV P y th a g o r e a n T r ip ıe s E x a m p ıe 3 B ıd e n t ııy ın s p y t h a g o
R jb +
.
爵树 寸e , 必 加 和匕
1) 4 , 5 , 6 1) 3 , 7 , 5
t e ll w h e th e r e a c h tr ia n g ıe d e s c r ib e d is a r ig h t tr ia n g le . t h e le n g th s o f th e th re e s id e s a re g iv e n .
O b h ı. Ł yy ıı
III.
A m X Ţ ' T Ï . , . h . . L is th e lo n g e s t s id e .
R e c a ll B y th e T ń a n g le I n e q u a lity T h e o re m , t h e s u M o f a ny
t w o s i d e l e ng
t h s o f a t r i a ng
l e i s g
r e a t e r t h a n t h e t h i r d s i d e l e ng
t h .
17 0 ; n o r ıw . .
s q u a r e s h o u ld J a n a c u t to m a k e th e ta b le c lo th ? R o u n d to th e n e a r e s t in c h .
d ia g o n a l o f th e ta b le c lo th to b e a n e x tr a 1 0 in c h e s s o it w ilı h a n g o v e r th e e d g e s o f th e ta b le . W h a t s iz e
Ja n a is c u ttin g a s q u a r e o f m a te ń a l fo r a ta b le c lo th . T h e ta b le'
s d ia g o n a l is 3 6 in c h e s . S h e w a n ts th e
E x a m p ıe 2
F in d th e v a lu e o f x . G iv e y o u r a n s w e r in s im p le s t ra d ic a l fo rm .
E x a m p ıe 1 A : F in d in g S id e L e n g th s in a 4 5 °
_ 4 5 °
_ 90 °
T ń a ng
l e
8
A
A C _ ß c _ ł A ß _ 1 l 2
o f a le g t im e s .
a n d t h e ıe n g t h o f t h e h y p o t e n u se is t h e le n g t h
In a 4 5 °
_ 4 5 °
_ 9 0 °
t r i a ng
ıe , b o t h le g s a r e c o n g r u e n ţ
T h e o r e m 5 - 8 - 1 $ 1 4 5 °
. 4 5 °
. 9 0 °
T r ıa ngle T h e o r e
A 4 5 °
. 4 5 °
. 9 0 °
t r i a ng
ıe i s o n e ty p
e o f W ·
a n is o s c e ıe s r ig h t t r ia n g ıe is a 4 5 °
_ 4 5 °
_ g o °
t r i a ng
l e .
o f a n is o s c e le s t r ia n g ıe a r e c o n g r u e n Ļ t h e m e a s u r e o f e a c h a c u t e a n g le is 4 5 °
. S o a n o t h e r n a m e f o r
a d ia g o n a ı o f a s q u a r e d iv id e s it in to tw o c o n g r u e n t is o s c e le s r ig h t t r ia n g le s . S in c e th e b a s e a n g le s
V I . 4 5 - 4 5 - 90 N O T E S
N ¢ lŁĻ / v>
S 、 、 !6 , ·[6 、 山
2×45
12
v e n v a lu e s c o u ld b e tiıe s id e s o f a 4 5 °
_ 4 5 °
_ 90 °
t r ia ng
l e .
2×46
Jt x iF
?x f+
F o r 1 3 - J5 , t e lt if th e g i \
10
9 .
I Q
: 11 h s e g m e n t
Z' "
7
\
圆 。J 2 1厚
四■ 歹 苴
3 1 8l 2
L e g 1 L e g 2 potenuse
1. C o m p le te th e fo llo w in g ta b le f o r th e 4 5 - 4 5 - 9 0 tń a n g le s u s in g e x a c t s im p lifie d r a d ic a l v a lu e s .
4 5 - 4 5 - 9 0 T ń a n g le s * *
D o n't f o r
ge t
yo u r b o o k w o r k ! !
N a m e : P e r io d
召
( · ÇA X C
/ , h , \
/ ı \
w ill y o u n e e d ? / I \h yp o te n u s e . A p p ro x im a te ly h o w m a n y p e g s
.. / I \S u p p o s e y o u m a k e a to o m w ith a n 1 8 - in c h / I \
a r e p la c e d e v e r y in c h a lo n g e a c h le g .
s tr ip s s h a p e d in to a 4 5 °
- 4 5 °
_ 9 0 °
t r i a ng
l e . P e g s fo rm .
2 0 . T h is tr ia n g le lo o m is m a d e fr o m w o o d 2 4 . G iv e n A C = 1 0 , fin d B X h ı s im p le s t r a d ic a l
14 y}tilvŢ
y ◆ 3 æ
e
L e a v e a n s w e r in s im p le s t r a d ic a l fo rm .
2 3 . S o lv e fo r th e fo llo w in g .
e 2 Ł, ţ c R
s im p le s t r a d ic a l f o rm
G iv e th e a n s w e r s in
d if e = 1 , e · 2 , a n d e = 3 .
a . F in d th e d ia g o n a l le n g th
舟ニ ルヌ伊ハユ
P - ţ Ļıin s im p le s t r a d ic a l f o r m .
d ia g o n a l le n g th 1 8 m e te r s . G iv e y o u r a n s w e r s
19 . F in d th e p e r im e te r a n d a r e a o f a s q u a re w ith
仵争 协 。了り
哆
G iv e y o u r a n s w e r s in s im p le s t r a d ic a l f o r m .
9 0 °
t ń a ng
l e w i t h a hy p
o [ e n u s e l e ng
t h 1 2 i n c h e s .
18 . F in d th e p e ń m e te r a n d a r e a o f a 4 5 °
_ 4 5 °
_
1 ñ Py
th e g r o u n d . A b o u t h o w lo n g is th e
14 5 fe e t u p th e to w e r . It fo r m s a 4 5 °
w ir e s u p p o r tin g a r a d io to w e r is
a n g le w ith th e g l
p o s itio n e d 1 4 5 f
17 . A g u y w ir e s
2 2 . E a c h e d g e o f th e c u b e h a s le n g th e .
X 4
Ą Dû $ T }
a p p r o x im a te a r e a o f th e g a r d e n ?
th e s e s e c tio n s is u s e d a s a g a r d e n . W h a t is th e
s e c tio n s a lo n g th e 4 0 f o o t d ia g o n a l . O n e o f
16 . S a m h a s a s q u a r e b a c k y a rd d iv id e d in to 2
2 1 . F in d th e v a lu e o f x in s im p le s t r a d ic a l f o r m .
B C = 5 l 3A C = s A B = 2 s
th e lo n g e r le g is t h e ıe n g t h o f t h e s h o r t e r ıe g t im e s 1 3 .
is 2 t im e s t h e le n g t h o f t h e s h o r t e r le g , a n d th e le n g tŁo f
ın a 3 0 °
. 6 0 °
_ 9 0 °
t r i a ng
l e , t h e ıe n g t h o f t h e h y p o t e n u s e is
Ħn d e . d " " · . D y . G i. ' " " " " . s i. p lc s t ' " . 1 fn - .
E x a n ıp le 1 D
1 5
F in d th e v a lu e s o f x a iıd y . G iv e y o u r a iıs w e r s in s im p le s t r a d ic a l f o r m .
E x a m p le 1 B
L�X - )
,
·
1 · ) 16
E . - p l, ıA F i. d in g S id e h n g s in ' " - 60 · 9 0 P m ' "°
吕
A C
e m 5 - 8 - 2 K 3 o °
- 6 o °
- 9 o °
T r ıa ngıe T h e o r e m
A 30 °
_ 60 °
_ 9 0 °
t r i a ng
l e i s a n o t h e r sp
e c i a l ńg
h t t r i a ng
l e .
1 . 3 0 - 6 0 - 9 0 N O T E S
N a m e
12 " .
12
f ill in th e b la n k s fo r th e s p e c ia l rig h t tria n g le s .
5 ·
6 ·
= ı 7 a b 7 øb m
7 m / 1o y 4 3
2 4 3 Ļ qrfL b 1 6 4 3 } 2
14■ 7 74
2 · 1 5 lııa a 10
Ì ) 【R rm
S h o r t L e g L o n g L e g H y p o te n u s e
C o m p le te th e ta b le fo r a 3 0 °
_ 6 0 °
_ 9 0 °
t r ia n g le u s in g e x a c t (r a d ic a l) v a lu e s .
1 . In a 3 o °
_ 6o °
_ 9 o °
t ń a n g le , t h e s h o r t le g is lo c a te d a c ro s s fr o m w h a t a n g le ? lm m æ
3 0 - 6 0 - 9 0 T r ia n g ıe s
P e r io d
fo r m .
2 7 . F in d Q R a n d P S .
N o
J , 3 , K
0_ 6 0
°. 9 0
° t r i a l ı
gl e .
뇨
J$ ) b , S(bJv怀 Ç一
ı y )
d ia g o n a 1?
is fo u r tim e s th e w id th . W h a t is th e le n g th o f th e
2 9 . T h e p e ń m e te r o f a re c ta n g le is 6 0 in . T h e le n g th
y > 3
X · y if į
>p U V Fs
s im p le s t r a d ic a l fo rm .
2 8 . S o lv e fo r th e fo llo w in g . L e a v e a n s w e r in
Q
S » Ra Ý ţ ?
tr
A n s w e r in s im p le s t ra d ic a l
ye s
20 . 4 6 , 2 , ó h
8 ft
p la tf o rm m u s t th e r a m p b e s e t?
th e p la tfo rm is 8 fe e t , h o w fa r a w a y fr o m th e
th e g r o u n d a t 3 0 °
. If th e h e ig h t fro m th e g ro u n d to
2 5 . A s k a te b o a r d r a m p m u s t b e s e t u p to ń s e fro m
A · y o i 1J'
Þ · b o F 1 Jtria n g le w ith h e ig h t 3 0 y a r d s .
2 4 . F in d th e p e ń m e te r a n d a r e a o f a n e q u ila te r a l
A · Ë ļ r 1 -
P . ) 2 6 ·
tr ia n g le w ith s id e le n g th 4 fe e t .
2 3 . F in d th e p e ń m e te r a n d a r e a o f a n e q u ila te ra l
tr ia n g le w ith h y p o te n u s e le n g th 2 8 c e n tim e te r s .
2 2 . F in d th e p e r im e te r a n d a r e a o f a 3 0 °
_ 60 °
_ 90 °
% Æ $,
*
F in d th e a r e a o f th e tr ia n g le .
2 1 . T h e h y p o te n u s e o f a 3 0 - 60 - 90 tria n g le is 1 2 42
18 . 9 ,
¢ l3 19 .17 . 2 , 2
. Y
/
43
C \
4
F o r 1 7 - 20 , t e lı if th e g iv e n v a in e s c o u ld b e th e s id e s o f a 3 0
â o
W o rk a n d A n s w e r (s )
F o rm u la msL· L L+ c \U s e
F in d th e le n g th o f e a c h s id e / \
C is th e c e n te r o f a r e g u la r h e x a g o n .8 ·
W o r k a n d A n s w e r ( s )
F o rm u la,
LL»L/ )ł> $ L- L
u se :_
W · b M ů
A D C
h e ig h t .
le n g th o f e a c h s id e a n d th e
p e ń m e te r 3 6 y u n its . Ħ n d th e
7 . A A B C is e q u ila te r a l w ith
5 4 3
543
C Wc w · ł}
3
W o r k a n d A n s w e r ( s )
F o m 俩 爾 闇
1 . u s e : m l s
3 ) S h o w w o r k a n d f in d a ll th e m is s in g s e g m e n t le n g th s
2 ) W r ite th e e q u a tio n o r p a t t e r n y o u w ill u s e
1) D e te rm in e if y o u s h o u ld u s e P y th a g o r e a n T h e o re m , 30 °
_ 6 0 °
_ 9 0 °
, o r 4 5 °
_ 4 5 °
_ 90 °
1. F o r e a c h p r o b le m
M ix e d A p p lic a tio n s - P r o b le m S o lv in g
N a m e : P e rio d
f u - \ F r o r % į . T O B Çy
c . H o w m u c h h ig h e r o n th e h o u s e d o e s th e lo n g e r b ra c e r e a c h th a n th e s h o r te r b r a c e ?
b ţ ケ · ¢ % 7 , ţ q ť ¢vb . H o w lo n g is th e lo n g e r b r a c e ?
s .
舟ちづ'杓 ·っすぢノ杓
A'
寺 o o
A Ĥ Į ų fiłi
W ill it fit i n 【p " i n
o n ly b o x th e y c o u ld f in d h a s d im e n s io n s o f 2 0 in x 1 6 in x 1 2 in . T h e p ip e th e y n e e d to s h ip is 2 4 in c h e s lo n g .
*1 3 . M a g ic p lu m b in g is n e e d in g to s h ip o u t a n e w w a te r p ip e to r e p la c e a b r o k e n o n e in th e S m ith
'
s h o u s e . T h e
3 $ F y p } $ ). H $a . H o w f a r a w a y fr o m th e h o u s e a r e th e b r a c e s p la c e d o n th e g ro u n d ?
s a n ıe s p o t, t h ey p
l a c e d a s e c o n d , lo n g e r b r a c e to m a k e a 3 0 °
a ng
l e w i t h t h e s i d e o f t h e h o u s e .
12 . A f te r h e a v y w in d s d a m a g e d a h o u s e , w o r k e r s p
l a c e d a 6 m . B r a c e a g a in s t its s id e a t a 4 5 °
a ng
l e . T h e n , a t t h e
m lr ¢ f % a ) . W ) Ç
W h a t is th e le n g th o f th e s lid e ?
1 1 . A s ıid e w a s in s ta lle d a t th e lo c a l s w im m in g p o o l , a s s h o w n h e r e
ヴ飞フ尸ナ
H o w f a r d o e s a p e r s o n tr a v e l fro m th e b o tto m to th e to p o f th e e s c a la to r ?
10 . A n e s c a la to r lif ts p e o p le to th e s e c o n d n o o r , 2 5 ft. A b o v e th e fır s t f lo o r . T h e e s c a la to r ris e s a t a 3 0 °
a ng
l e .
O , ą F y
o f tw o a d ja c e n t b la d e s is 3 6 ft . H o w lo n g is e a c h b la d e ? R o u n d y o u r a n s w e r to th e n e a r e s t te n th .
9 . T h e fo u r b la d e s o f a h e lic o p te r m e e t a t ń g h t a n g le s a n d a r e a ll th e s a m e le n g th . T h e d is ta n c e b e tw e e n th e tip s
D r a w a p ic tu r e ií o n e is n o t g iv e n a n d s o lv e th e p r o b le m .