n p i 1 h ;?anyp y b ć n th...170 ; n o r ıw. . sq u are sh o u ld jan a cu t to m ak e th e ttab...

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1 \ ' : ° Ų th e h yp otenuse? w E x . 2 a ) W hat v aria b ıe re p re s e n ts b ) If p - 2 5 a n d r - 2 4 th e n w - . P th e h yp o te n use? E x . 1 a ) W hat v a r ia b le re p re s e n ts r b ) If p - 8 a n d r - 1 5 th e n w - . U U i s th e ! ņ ¢ ( l o n g e s t s id e ) . a s y o u k no w th e o ther h n s id es . Th e p y th a g o re an T h e o re m is . D y b ' = ć w h e re 1. In a X ' '" th . ." ;?anyp s s in g s id ' '" ' " I ntro d u c tio n to P y th a g o re a n T heorem N a m e : . P e rio d 1 1/10/2 0 0 8 G L

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Page 1: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

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

Page 2: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

5 ) 6 , 9 , 6

只づ知卜

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If c z > a

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. T h e n ö A ß C l s

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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

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ÝR.

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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 +

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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 .

Page 3: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

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

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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 .

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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 °

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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

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T r ıa ngle T h e o r e

A 4 5 °

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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 °

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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

Page 4: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

N ¢ lŁĻ / v>

S 、 、 !6 , ·[6 、 山

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v e n v a lu e s c o u ld b e tiıe s id e s o f a 4 5 °

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t r ia ng

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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

Page 5: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

( · ÇA X C

/ , h , \

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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

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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 .

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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

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9 0 °

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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 °

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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 .

Page 6: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

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 .

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T r ıa ngıe T h e o r e m

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t r i a ng

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e c i a l ńg

h t t r i a ng

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1 . 3 0 - 6 0 - 9 0 N O T E S

Page 7: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

N a m e

12 " .

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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

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S h o r t L e g L o n g L e g H y p o te n u s e

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_ 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

Page 8: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

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 .

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

/

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Page 9: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

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 )

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u se :_

W · b M ů

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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

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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 °

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, o r 4 5 °

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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

Page 10: N P I 1 h ;?anyp y b ć n Th...170 ; n o r ıw. . sq u are sh o u ld Jan a cu t to m ak e th e ttab leclo th ? R o u n d to h e n eare st in ch. diag o n al o f th e gtab l eclo th

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 .