41 R

ight

Tri

angl

e T

rigo

nom

etry

Knight’s Charge:

Pre

calc

ulus

1

41 R

ight

Tri

angl

e T

rigo

nom

etry

Check Homework:

Pre

calc

ulus

2

41 R

ight

Tri

angl

e T

rigo

nom

etry

Check Homework:

Pre

calc

ulus

3

40x

41 R

ight

Tri

angl

e T

rigo

nom

etry

Check Homework:

Pre

calc

ulus

4

Sec 4.1:Right Triangle Trigonometry

Objectives:Evaluate trigonometric functions of acute anglesUse the fundamental trigonometric identitiesUse trigonometric functions to model and solve real-life problems

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

6

41 R

ight

Tri

angl

e T

rigo

nom

etry

Trigonometric Functions

Pre

calc

ulus

7

opp

adj

hyp

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

8

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

Example 1

• Evaluate the six trig functions of the angle shown in the right triangle

• sin =

• cos =

• tan =

• csc =

• sec =

• cot =

Pre

calc

ulus

9

5

12

13

41 R

ight

Tri

angl

e T

rigo

nom

etry

YOU TRY

• Evaluate the six trig functions of the angle shown in the right triangle

• sin =

• cos =

• tan =

• csc =

• sec =

• cot =

Pre

calc

ulus

10

41 R

ight

Tri

angl

e T

rigo

nom

etry

Example 2

Find if

Pre

calc

ulus

11

41 R

ight

Tri

angl

e T

rigo

nom

etry

You Try

Find if

Pre

calc

ulus

12

41 R

ight

Tri

angl

e T

rigo

nom

etry

Example 3• Evaluating the following to the nearest hundredths using a

calculator:

Pre

calc

ulus

13

41 R

ight

Tri

angl

e T

rigo

nom

etry

Example 4• Find the value of x for the right triangle shown

Pre

calc

ulus

14

x

15

30°

41 R

ight

Tri

angl

e T

rigo

nom

etry

Example 5• Solve ∆ABC (i.e. find the measures of all the unknown angles

and sides of the triangle).

Pre

calc

ulus

15

A

B

C

62°

6c

b

41 R

ight

Tri

angl

e T

rigo

nom

etry

You Try• Solve ∆ABC.

Pre

calc

ulus

16

A

B

C30°

ac

15

41 R

ight

Tri

angl

e T

rigo

nom

etry

Example 6• Find the measure of angle B to the nearest tenth (ONE decimal

place ).• .

Pre

calc

ulus

17

A

B

C

915

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

You Try

Find the measure of angle A to the nearest hundredths (TWO decimal places ).

Pre

calc

ulus

18

A

B

C

12

15

41 R

ight

Tri

angl

e T

rigo

nom

etry

Example 7• Solve ∆ABC (i.e. find the measures of all the unknown angles

and sides of the triangle).

Pre

calc

ulus

19

A

B

C

9c

5

41 R

ight

Tri

angl

e T

rigo

nom

etry

You Try• Solve ∆ABC.

Pre

calc

ulus

20

A

B

C

12

2

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

21

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

22

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

23

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

24

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

25

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

26

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

27

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

28

41 R

ight

Tri

angl

e T

rigo

nom

etry

Pre

calc

ulus

29

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

30

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

Victory Lap

Find the unknown value:

Pre

calc

ulus

31