1 RATIOS IN RIGHT TRIANGLES OPPOSITE SIDE? ADJACENT SIDE? HYPOTENUSE? SINE? COSINE? TANGENT?...

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RATIOS IN RIGHT TRIANGLES

OPPOSITE SIDE?ADJACENT SIDE?

HYPOTENUSE?

SINE? COSINE? TANGENT?

Standards 15, 18, 19

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Standard 15:

Students use the pythagoream theorem to determine distance and find missing lengths of sides of right triangles.

Los estudiantes usan el teorema de Pitágoras para determinar distancia y encontrar las longitudes de los lados de teoremas rectángulos.

Standard 18:

Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them, (e.g., tan(x)=sin(x)/cos(x), etc.)

Los estudiantes conocen las definiciones de las funciones básicas trigonométricas definidas para los ángulos de triángulos rectángulos. Ellos también conocen y son capaces de usar relaciones básicas entre ellos. (ej., tan(x)=sin(x)/cos(x), etc.)

Standard 19:

Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.

Los estudiantes usan funciones trigonométricas para resolver para una longitud desconocida de un triángulo rectángulo, dado un ángulo y la longitud de un lado.



3

ADJACENT

SIDE

HYPOTENUSE

Standard 18



4

OPPOSITE

SIDE

Standard 18



5

ADJACENT

SIDE

HYPOTENUSE

Standard 18



6

OPPOSITE

SIDE

Standard 18



7

ADJACENT

SIDE

HYPOTENUSE

Standard 18



8

OPPOSITE

SIDE

Standard 18



9

ADJACENT

SIDE

HYPOTENUSE

Standard 18



10

OPPOSITE

SIDE

Standard 18



11

ADJACENT

SIDE

HYPOTENUSE

Standard 18



12

OPPOSITE

SIDE

Standard 18



13

ADJACENT

SIDE

HYPOTENUSE

Standard 18



14

OPPOSITE

SIDE

Standard 18



15

b

a

c

C

B

A

The ADJACENT side to A is side “b” or CA

Standard 18



16

b

a

c

C

B

A

The OPPOSITE side to A is side “a” or BC

Standard 18



17

k

m

l

L

K

M

What is the adjacent side to M?

The ADJACENT side to M is side “k” or LM

Standard 18



18

What is the opposite side to M?

The OPPOSITE side to M is side “m” or KL

k

m

l

L

K

M

Standard 18



19

r

t

s

S

R

T

What is the adjacent side to R?

The ADJACENT side to R is side “t” or RS

Standard 18



20

What is the opposite side to R?

The OPPOSITE side to R is side “r” or ST

r

t

s

S

R

T

Standard 18



21

zx

y

Y

ZX

What is the adjacent side to X?

The ADJACENT side to X is side “y” or XZ

Standard 18



22

What is the opposite side to X?

The OPPOSITE side to X is side “x” or ZY

zx

y

Y

ZX

Standard 18



23

b

ac

R

Q

S

What is the adjacent side to S?

The ADJACENT side to S is side “b” or RS

Standard 18



24

b

ac

What is the opposite side to S?

The OPPOSITE side to S is side “a” or QR

R

Q

S

Standard 18



25

o

u

i

C

B

A

What is the adjacent side to C?

The ADJACENT side to C is side “o” or CA

Standard 18



26

C

B

A

What is the opposite side to C?

The OPPOSITE side to C is side “i” or AB

o

u

i

Standard 18



27

e

i

u

Q R

S

What is the adjacent side to Q?

The ADJACENT side to Q is side “e” or QS

Standard 18



28

What is the opposite side to Q?

The OPPOSITE side to Q is side “u” or RS

e

i

u

Q R

S

Standard 18



29

o

u

i

C

B

A

Sin C =

Sin C=Hypotenuse

Opposite side

SINE

u

i

Standard 18



30

o

u

i

C

B

ACos C =

Cos C=Hypotenuse

Adjacent side

COSINE

u

o

Standard 18



31

o

u

i

C

B

A

Tan C =

Tan C=Adjacent side

Opposite side

TANGENT

i

o

Standard 18



32

o

u

i

C

B

A

Tan C=i

o

Tan C=Adjacent side

Opposite side

TANGENT

Sin C=i

u

Sin C=Hypotenuse

Opposite sideSINE

Cos C=o

u

Cos C=Hypotenuse

COSINEAdjacent side

Standard 18



33

b

a

c

C

B

A

Sin A =

Sin A=

a

Opposite side

c

Hypotenuse

Standard 18



34

b

a

c

C

B

A

Cos A =

Cos A=

c

Hypotenuseb

Adjacent side

Standard 18



35

b

a

c

C

B

A

Tan A=

Tan A=

a

Opposite side

Adjacent side

b

Standard 18



36

b

a

c

C

B

A

Sin B =

Sin B=

c

Hypotenuse

b

Opposite sideStandard 18



37

b

a

c

C

B

A

Cos B =

Cos B=

c

Hypotenusea

Adjacent side

Standard 18



38

b

a

c

C

B

A

b

Opposite side

Adjacent

cTan B =

Tan B=

Standard 18



39

km

l

L

KM

Sin M =

Sin M=

k

Hypotenuse

m

Opposite side

Standard 18



40

km

l

L

KM

Cos M =

Cos M=

k

Hypotenusel

Adjacent side

Standard 18



41

km

l

L

KM

Tan M=

Tan M=

m

Opposite side

Adjacent

l

Standard 18



42

km

l

L

KM

Sin L=

Sin L=

k

Hypotenuse

l

Opposite side

Standard 18



43

km

l

L

KM

Cos L =

Cos L=

k

Hypotenusem

Adjacent side

Standard 18



44

km

l

L

KM

Tan L =

Tan L=Adjacent

m

l

Opposite side

Standard 18



45

r

ts

S

R

T

Sin T=

Sin T=

s

Hypotenuse

t

Opposite side

Standard 18


46

r

ts

S

R

T Cos T=

Cos T=

s

Hypotenuser

Adjacent side

Standard 18


47

r

ts

S

R

T

Tan T =

Tan T=

t

Opposite side

Adjacent

r

Standard 18


48

r

ts

S

R

T

Sin R =

Sin R=

s

Hypotenuse

r

Opposite side

Standard 18


49

r

ts

S

R

T Cos R =

Cos R=

s

Hypotenuset

Adjacent side

Standard 18


50

r

ts

S

R

T

Tan R =

Tan R=Adjacent

t

r

Opposite side

Standard 18


51

4

3

5

YZ

X

Sin Z =

Sin Z=

5

Hypotenuse

4

Opposite side

Sin Z= 0.8

Standard 18Find Sin Z:


52

YZ

X

Cos Z =

Cos Z=

5

Hypotenuse3

Adjacent side

4

3

5

Cos Z= 0.6

Standard 18Find Cos Z:


53

YZ

X

Tan Z =

Tan Z=

4

Opposite side

Adjacent

34

3

5

Tan Z= 1.3

Standard 18Find Tan Z:


1 RATIOS IN RIGHT TRIANGLES OPPOSITE SIDE? ADJACENT SIDE? HYPOTENUSE? SINE? COSINE? TANGENT?...

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Transcript of 1 RATIOS IN RIGHT TRIANGLES OPPOSITE SIDE? ADJACENT SIDE? HYPOTENUSE? SINE? COSINE? TANGENT?...