9.5 Trigonometric ratios

How are trigonometric ratios used to find missing sides of right

triangles?

• Trig ratio- ratio of the lengths of two sides of a right Δ. Used to find missing side lengths when only 1 length is known.

• Always round to four decimal places

38°

12

3 basic trig ratios• Sine (sin)

• Cosine (cos)

• Tangent (tan)

• Sin

• Cos

• Tan

hypot

sideOpp .

hypot

sideadj .

adj

opp

Just remember Chief…

SOH CAH TOAine

ppos i te

ypotenus

osine

dj acent

ypotenus

angent

ppos i te

dj acent

Ratios of s A and BA B

c

aAsin

c

bAcos

b

aAtan

c

bB sin

c

aB cos

a

bB tan

A

BC a

bc

Ex: Find sin, cos, & tan of A & B. A

sin A= 12/13 = .9231

cos A= 5/13 = .3846

tan A= 12/5 = 2.4

B

sin B= 5/13 = .3846

cos B= 12/13 = .9231

tan B= 5/12 = .4167

C

A

B

13

12

5

Example

30

60__

__

1

2

A

BC

3

sin A= ½ or .5

sin 30= .5

Find sin A and sin 30o.

Example

45

45__

__A

BC1

12

7071.2

2or

2

1 sin B

sin 45o =.7071

Find sin B and sin 45o.

• Using your calculator find

tan 23

sin 72

cos 44

Assignment

Trigonometric Ratios WS #1-24

Use trig to solve for n.

35

8

m

n

Use trig to solve for m.

35

8

m

n

Use trig to find t.

72

13

z

t

Use trig to find z.

72

13

z

t

Angle of elevation

ground

angl

e of

ele

vatio

n

ExampleFind the height of the tree

48o

100 ft

__

__

h

You are given the adj side & finding the opp side.

Use tangent!!

tan 48o = h/100

111.06 = hAbout 111 ft

100 tan 48o = h

Example

100ft

30o

d

__

__

Have opp side need hypot

Use sine!!

do 1000

30sin .5d=1000

d=2000 ftd

10005.

Assignment

Trigonometry WSTrigonometry WS#1-18#1-18