Right Triangle Trigonometry Objectives: Evaluate trigonometric functions of acute angles Use the fundamental trigonometric identities Use trigonometric.

Right Triangle Trigonometry

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

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

2

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

Trigonometric Functions

Pre

calc

ulus

3

opp

adj

hyp

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

4

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

5

5

12

13

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

YOU TRY

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

• sin =

• cos =

• tan =

• csc =

• sec =

• cot =

Pre

calc

ulus

6

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

Example 2

Find if

Pre

calc

ulus

7

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

You Try

Find if

Pre

calc

ulus

8

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

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

calculator:

Pre

calc

ulus

9

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

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

Pre

calc

ulus

10

x

15

30°

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

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

and sides of the triangle).

Pre

calc

ulus

11

A

B

C

62°

6c

b

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

You Try• Solve ∆ABC.

Pre

calc

ulus

12

A

B

C30°

ac

15

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

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

place ).• .

Pre

calc

ulus

13

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

14

A

B

C

12

15

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

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

and sides of the triangle).

Pre

calc

ulus

15

A

B

C

9c

5

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

You Try• Solve ∆ABC.

Pre

calc

ulus

16

A

B

C

12

2

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

17

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

18

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

19

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

20

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

21

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

22

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

23

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

24

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

25

4.3

Rig

ht T

rian

gle

Tri

gono

met

ryP

reca

lcul

us

26

4.3

Rig

ht T

rian

gle

Tri

gono

met

ry

Victory Lap

Find the unknown value:

Pre

calc

ulus

27