Trig SOH CAH TOAA

C B

WHICH HOUSE WOULD YOU RATHER LIVE IN?

House number 1 OR House number 2?

House number 1

House number 2

Trigonometry

Trig means angle measurement

Trig deals with the relation between sides and angles

Trig helps you find the length of a side or the measure of an angle

What might you use trig for?

Is your ladder long enough to reach the gutters?

What is the shortest distance between two points?

What is the height and width of a TV screen?

Where will your furniture fit in a room?

What is the height of a building or a tree?

How can you build a staircase?

To build a house correctly

Trigonometric RatiosSine Sin = _opposite_ hypotenuse Cosine Cos = _adjacent_ hypotenuse

Tangent Tan = opposite adjacent

Trig Memory Clue

SOH CAH TOA

S ine C osine T angent O pposite A djacent O pposite H ypotenuse H ypotenuse A djacent

SIN, COS, and TANFind sine, cosine, and tangent of acute

angles only.A

BC

2

3

5

Sin =

Cos =

Tan =

A

A

A

Sin =

Cos =

Tan =

B

B

B

Sin

Cos

Tan

Sin

Cos

Tan

T L

G

F

B

R

3

6

6.7

14

11

17.8

Y

O

U

AR

E

X

Y

Z

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

7

11.4

11

9

14.2

612

13.49

…for the red acute angle only.

PRACTICE SIN, COS, and TANA

H

N

CS B

Sin

Cos

Tan

Sin

Cos

Tan

1. 2. 3.

LT

A

6

810

12 13

5

2425

7

Sin

Cos

Tan

…for both acute angles.

H A

M

R

IB

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

6.27.1

3

3

3 2

3.5

A

M

A

M

A

M R

R

R

B

B

B

N

D

YJ

L

P

C

W

V

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

4. 5.

6.

9

12 15

16

12

20

9

16

13

7. 8.

9.

P

I

YT

E

Q

A

DG

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

724

25

1024

26

3

4

5

10. 11.

12.

G

I

F

E

C

T

S

Z

OSin

Cos

Tan Sin

Cos

Tan

Sin

Cos

Tan

6 10

8

10

26

24

15

25

20

13. 14.

15.

S

F

H

K

M

B

C

W

I

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

12

3 1

1

2

2

4

2 5

16. 17.

18.

L

O

M

U

B

T

F E

D

Sin

Cos

TanSin

Cos

Tan

Sin

Cos

Tan

6.2

7.8 10

6.2

3.5

7.1

4.3

4.7

6.4

19. 20.

21.

Q

Z

A

E

D

C

T

G

B

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

4.1

5.6

7

5

6

7.8

16

30

34

22. 23.

24.

Sin

Cos

Tan

Sin

Cos

Tan

Sin

Cos

Tan

JI

B

C

A

R

L

O

G

25 24

32

24

32

40

50

48

14

What is the hypotenuse?

It is always across from the right angle.It is always the longest side.

hypotenuse

HypotenuseA

EGE

L

A

A

B

C A

G

L

Practice marking the hypotenuseA

B

G

I

H

K

LD

E

J

C

F

1. 2.

3. 4.

Practice marking the hypotenuseA

B

CA

BC A

A

B

B

C

C

5. 6.

7. 8.

Practice marking the hypotenuse

A

B

C

9.

10.

C

B

A

A

B

11.

CA

B

C12.

What is the opposite side?

It is the side across from the angle you’re working with.

A

C B

The side opposite is

A

CB

The side opposite is

B

AC

Opposite Side

N

O

PK

I

M

S

D M

J

D

V

Side opposite

Side opposite

Side opposite   Side opposite

Side opposite Side oppositeSide opposite

Side opposite

N

P

K

I

S

M

V

D

Practice marking opposite sideA

TC

A

BCA

B

D

G

D O

1. 2.

3. 4.

Practice marking opposite side

D

L

EY

GO

C

W

R

P

D

I

5. 6.

7.8.

Practice marking the opposite side

A

D

F

9. 10.

G

M

U

G

Z I11.

12.

Z

D

A

What is the adjacent side?

The adjacent side runs alongside the angle (but it won’t be the hypotenuse).

A

B

C

The side adjacent to is

A

AC

The side adjacent to is

B

BC

Practice marking the adjacent side

A

B

C

A

RC

A

O

P

B

G

1. 2.

3. 4.

M

Side adjacent to

Side adjacent to

Side adjacent to

Side adjacent to

Side adjacent to

Side adjacent to Side adjacent to

Side adjacent to

<B

<A

<P

<O

<R

<A

<A

<B

Practice marking the adjacent sideF

I R

AP

L

E

D

B

D

N

U

5. 6.

7. 8.

Practice marking the adjacent sideO

G

U

G

F

D

S

A

G

NW

U9. 10.

11. 12.

STRAW ACTIVITYYou will be given 3 straws and a piece of poster board.

Place the straws on the poster board in the shape of a right triangle

Label the angles with your initials

Label the hypotenuse

I will come around and give you one of the angles: You will label the opposite side and the adjacent side

STRAW ACTIVITY EXAMPLE

L

A T

hypotenuse

Using angle L, label the opposite and adjacent sides

opposite

adjacent

Practice marking different sides1.

H

T

E

2.

A

D

Y3. S

O

I

4.

V

R

E

5.

6.

7.

8.

A

A A

A

P

M

T

P

N

P

C

P

9.T

O

N

10.

Y

O

U

11.S

K

J

12.

M

A V

13.

A

C

E

14.

J

M

A

15. N E

W

16.

O

L

D

17. 18.

19.20.

Q

W E

R T

Y

A

S D

F

G

H

21. 22.

23. 24.

LK

J

M N

B

P

O

I

V

C

X