RIGHT TRIANGLESSine, Cosine, Tangent

8.7 Sine, Cosine, And Tangent

Essential Question: How do you find the side lengths of a triangle that is not special?

opposite adjacentStudy of ∆s and relationships between

their angles and sides

• Angles are labeled with uppercase (ex. A)• sides are lowercase (ex. a)

• An angle and its opposite side use the same letter (ex. A and a)

OH

AOHA

SOH CAHTOA Sine=

Cosine=Tangent=

OH

AH

OA

When finding sin, cos, tan…1. Solve for missing sides2. Mark angle you are using3. Label opp. (O), adj. (A), hyp. (H)4. Write sin, cos, tan ratios5. Rationalize/simplify

OHA 13

222 cba 222 125 c

13c

HOAsin

HAAcos

AOAtan

1312

12135

5

O

H A10√2

222 cba 222 155 b

200c

HOB sin

HAB cos

AOB tan

1510√2

10√2

155

5210c

322

31

22

12

6√3O

H

AHO

30sin

HA

30cos

AO

30tan

126

21

1236

23

366

31

33

Technology Break5min

8.8 Trig Ratios with a Calculator

Essential Question: How do you find side lengths of a triangle that is not special?

= 0.9781= 0.5= 0.2679

When solving for missing sides…1.Mark angle you are working

with2.Label O, A, and H3.SOH? CAH? Or TOA?4.Set-up and solve for missing

side.O

H

ATo find a:CAHTo find b:SOH3022 a

cos

a)(cos2230a827.

3022 bsin

b)(sin2230b211.

SOH CAHTOA

OH

A

To find c:CAHTo find d:TOA

c942cos

429

cosc

112.c

942 dtan

d)(sin429

d18.

Plicker Exit SlipQuestion 1:What is sin(A)?

A)

B)

C)

D)

Question 2:What is tan(25)?

Round to the hundredths.

A) 0.42B) 0.46C) 0.47D) 0.91

√17

2√25

Homework 8.7 ALL 8.8 ALL