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yth a g o r e a n T h e o r e m m o r e th a n

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=JS o m e tim e s th e

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_ . . . . . . . _ _ . .

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II . H id d e n a n d D o u b le P y t h a g o r e a n T h e o r e m - R o u n d a lı a n s w e r s to th e n e a r e s t h u n d r e d th s .

6

y d .

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th e h y p o te n u s e ?

E x . 2 a ) W h a t v a r ia b ıe r e p r e s e n ts b ) If 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 . Ia ) 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 =

is th e (lo n g e s t s id e ) .

a s y o u k n o w th e o th e r. . . _ . . . . . . . .

s id e s . T h e P y th a g o re a n T h e o r e m is.

w h e r e

In a_ - _ . . . . . . .

Tr ia n g le , y o u c a n u s e th e to s o lv e fo r a n y m is s in g s id e a s lo n g

I P y th a g o r e a n T h e o r e m

In tr o d u c tio n to P y th a g o r e a n T h e o r e m

N a m e P e ń o d 1 1 / 1 0 /2 0 0 8 G L

4 . 1 1 , 18 , 34

T e ll if th e m e a s u re s c a n b e th e s id e le n g th s o f a tr ia n g le . If s o , c l a s s i fy

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l e a s a c u t e , o b t u s e , o r r i gh t .

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- 2 [ p y th ıg m ın ın * q u ıık * s T h · o r» m )

V P y th a g o r e a n I n e q u a litie s

E x p ıa ın .

4 8a P y t h a g o r e a n t r ip ıe .

E x a m p ıe 3 M ıd e n t ıfy ın g P y w h a g o r e a n T rıp ıe s

臺屋出国國 1 2 , 1 3 , 8 ,1 5 , 1 7 园里王四困国I1

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E y th a a o r e a n t r io ıe ,

a n d c s u c h t h a t a2 + b

2 . c2

is c a l le d a

12

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E x p la ın .

a p y t h a g o r e a n t r lp ıe .

T e ıı If t h e s id e ıe n g t h ı f o r m

IV P y th a g o r e a n T r ip le s

F ın d t h e m ıs s ın g s id e ıe n g t h .

E x a m p ıe 3 o ıd e n t il w n a p y w h a g o r e a n T r ıp ıe *

4 ) 1 , 2 , 45 5 ) 6 , 9 , 6 6 ) 4 2 , l3 , 4 5

1) 4 , 5 , 6 2 ) 6 , 8 , 10 3 ) 3 , 7 , 5

t e ll w h e th e r e a c h tr ia n g le d e s c r ib e d is a rig h t tria n g le . t h e le n g th s o f th e th r e e s id e s a r e g iv e n .

E x . n 5 , 1 6 , 1 5 E x . 2 ) 3 , 5 , 43l

A tr ia n g le is a tr ia n g le if + -_ . . . . . - . . '

w h e n is th e lo n g e s t s id e .

m . D e te r m in in g if a t r ia n g le is a r ig h t t r ia n g ıe .

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 .

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 ill 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 . v d . . o f . . C l" y o ' " " in s im p l' " a d i c d fo ", 八 。

E · - p l' "

L�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 f o rm .

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_ 4 5°

_ 90 °

T r i a ng

l e

A

A C _ B c _ t A ß . T l 2

o f a le g t im e s l 2 .

a n d t h e ıe n g t h o f t h e h y p o t e n u s e is t h e le n g t h

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t r i a ngle , b o t h ıe g s a r e c o n g r u e n t ,

B

o r e m 5 - 8 - 1 9 1 4 5 °

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t r i a ng

l e i s o n e ty p

e o f

a n is o s c e ıe s r ig h t t r ia n g le 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 t , t h e m e a s u r e o f e a c h a c u t e a ng

l e i s 4 5 °

. S o a n o th e r n a m e fo r

a d ia g o n a l 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 ıe s

V l . 4 5 - 4 5 - 90 N O T E S

F o r 1 3 - J5 , t e l l if th e g iv e n v a ıu e s c o u ld b e th e s id e s o f a 4 5 °

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t r ia ng

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A X C

w ill y o u n e e d ?

,, / I \h yp o te n u s e . A p p r o x im a te ly h o w m a n y p e g s

S u p p o s e y o u m a k e a lo o m w ith a n 1 8 - in c h

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 f o 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 , f ın d B X i n s i mp

l e s t r a d i c a t

in 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 ń m e te r a n d a r e a o f a s q u a r e w ith

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 r i a ng

l e w i t h a hy p

o t e n u s e l e i ıg

t h 1 2 i n c h e s .

18 . F in d th e p e r im e te r a n d a r e a o f a 4 5 °

_ 4 5 °

_

了八

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 f o r th e fo llo w in g .

w ir e ? s im p le s t ra d ic a l f o rm .

a n g le w ith th e g r o u n d . A b o u t h o w lo n g is th e G iv e th e a n s w e rs in

p o s itio n e d 1 4 5 fe e t u p th e to w e r . It fo r m s a 4 5 d if e = ı , e . 2 , a n d e

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,

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

a p p ro x im a te a r e a o f th e g a rd 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 fo 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 re b a c k y a r d d iv id e d in to 2

2 1 . Fi n d th e v a lu e o f x in s im p le s t ra d ic a l fo rm .

B C = 5 l 3A C = s A B = 2 s

th e ıo n g e r ıe 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

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_ 6 0 °

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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

白 丁

247/ i

F in d th e v a lu e s o f x a n d y . 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 fo r m .

E x a m p le 1 D

ダ

30 °

\\

5

F in d th e v a lu e s o f x a n d y . 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 rm

x

E x a m p le 1 C

1 5

F in d th e v a lu e s o f x a n d y . 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 .

E x a m p ıe 1 B

ダ

h 3 0 °

,

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6 0

E x a m p le 1 A F in d in g S id e L e n g th s in a 3 00

- 6 0°

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T ń a ng

l e

N _

A C

o r e m 5 - 8 - 2 g ( 3 o °

_ 6 o °

. 9 o °

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A 30 °

_ 60 °

_ 9 0 °

t r i a ng

l e i s a n o t h e r sp

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h t t r i a ng

l e .

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

12

9 t

1 4

12

9 .

― ―

10

_ ― ― 丁丁歹ダ

f ill in th e b la n k s fo r th e s p e c ia l r ig h t tr ia n g le s .

8 . 7 a b

■ 1 1 10 y l3

= ı 9

■ 2 4 3

U 6 4 3

14■ 1圜 团团国

四■

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

C o m p le te th e ta b le fo r a 3 0'

, 60'

, 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 0'

. 6 0 °

- 9 0 °

t r ia 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 ?

3 0 - 6 0 - 90 T r ia n g le s

X

2 6 . F in d th e v a lu e o f x in s im p le s t ra d ic a l fo r m ,

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 . Th e le n g th

S l

2 8 . S o lv e f o r th e f o llo w in g . L e a v e a n s w e r in

p la tfo r m m u s t th e r a m p b e s e t?

th e p la tf o rm is 8 fe e t , h o w fa r a w a y fr o m th e

th e g ro u n d a t 3 0 °

. If th e h e ig h t fr o m th e g r o 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 r is e fr o m

tria 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 rim e te r a n d a r e a o f a n e q u ila te r a l

tń a 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 re a o f a n e q u ila te r a l

tria 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 rs .

2 2 . F in d th e p e ń m e te r a n d a r e a o f a 3 0 °

_ 60 °

_ 90 °

ft. F in d th e a r e a o f th e tr ia n g le .

Fo rm .

2 1 . T h e h y p o te n u s e o f a 3 0 - 60 - 90 tń a n g le is 1 2 4 2 2 7 . F in d Q R a n d P S . A n s w e r in s im p le s t ra d ic a l

17 . 2 , 2 4 3 , 4 18 . 9 , 3 , 34 3 19 . I3 , 3 , 46 20 . 4 4 6 , 2 4 6 , 6l 2

F o r 1 7 - 2 0 , t e ıł t h e g

i v e n v a ıu e s c o u ld b e th e s id e s o f a 3 0 °

_ 60 °

_ 9 0 °

t r i a ng

ıe .

W o rk a n d A n s w e r (s )

F o rm u la

4 &

W o r k a n d A n s w e r ( s )

F o r m u la :

2 . U s e

w o rk a n d A n s w e r (s ) : 3 o

,

c

F o rm u la 33

CU s e :

/ \F in d th e le n g th o f e a c h s id e

8 . C is th e c e n te r o f a re g u ıa r h e x a g o n .

A Dh e

I :_

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 . F ın d th e

7 . M B C is e q u ila te r a l w ith l l\Ā

5 4 3

W o r k a n d A n s w e r ( s ) : W o r k a n d A n s w e r ( s )

F o r m u la F o rm u la

5 . U s e : 6 . U s e

Y į '

A n s w e r (s ) :

543

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0

C W

L�W o r k a n d A n s w e r ( s )

F o r m u la

1 . U s e

3 ) S h o w w o r k a n d fın d a ll th e m is s in g s e g m e n t le n g th s

2 ) W ń te 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 wh a g o r e a n T h e o re m , 30 °

_ 6 0 °

_ 9 0 °

, o r 4 5 °

_ 4 5 °

_ 9 0 °

1. F o r e a c h p ro 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 r io d :_ . ― ― . "

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 r a c e re a c h th a n th e s h o r te r b r a c e ?

b . H o w lo n g is th e lo n g e r b r a c e ?

W ill it flit in th e b o x ? E x p la in y o u r a n s w e r .

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 tıe e d to s h ip is 2 4 in c h e s lo n g .

41 3 . M a g ic p lu m b in g is n e e d in g o s h ip o u t a n e w w a t e r ip e o r e 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

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 r o u n d ?

s a n ıe s p o t, th e y p la 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 出 血 t h e s i d e o f t h e h o u s e .

12 . A fte 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 rs p la 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

W n a t is th e le n g th o f th e s lid e ?

1 1 . A s lid 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 re

H o w f a r d o e s a p e r s o n tr a v e l fr o m th e b o tto m to th e to p of th e e s c a la to r ?

10 . A n e s c a la to r lifts p e o p le to th e s e c o n d flo o r , 2 5 ft. A b o v e th e fırs l 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 f tw o a d ja c e n t b la d e s is 3 6 f t . 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 r ig 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 t u r e if 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 .