Lesson 13.1 Right Triangle Trigonometry

Hypotenuse

Adjacent LegO

pp

osit

e

Leg

SOH hyp

oppsin

CAH hyp

adjcos

TOA adj

opptan

sin

1csc

opp

hyp

cos

1sec

adj

hyp

tan

1cot

opp

adj

Finding Exact Values 30-60-90

30sin

30cos

30tan

30°

60°1

2

3

60sin

60cos

60tan

2

1

2

3

3

3

3

1

2

3

2

1

3

Finding Exact Values 45-45-90

45sin

45cos

45tan

2

2

2

2

2

45°

45° 22

45°

45°1

2

1

12

2

Example 1 Find Trigonometric Values

sin

cos

tan

csc

sec

cot

[A]

3

4

5

5

4

5

3

3

4

4

5

3

5

4

3

Example 1 Find Trigonometric Values

sin

cos

tan

csc

sec

cot

[B]

5

12

13

13

5

13

12

12

5

5

13

12

13

5

12

Example 2 Use one Trig Ratio to find others

cos

?cot

[A]5

2

Example 2 Use one Trig Ratio to find others

tan

?sec

[B]3

5

5

3

34

34

532

222

h

h

h

34

3

34sec

adj

hyp

Example 3 Find missing sides of Right Triangles Calculator Free

[A]8

30°

x

SOHCAHTOA

Example 3 Find missing sides of Right Triangles Calculator Free

[B]

12

60° x SOHCAHTOA

383

324xx

1260sin

x12

23

243 x

324x

Example 3 Find missing sides of Right Triangles Calculator Free

[C]

1245°x

SOHCAHTOA

Example 3 Find missing sides of Right Triangles Calculator Free

[D]

1045°

x

SOHCAHTOA

1045sin

x

2102 x

1022 x

25x

Example 4 Solve a Triangle

1035°

A B

CAnglesA =B =C =

Sidesa = b =c =

Solve triangle ABC. Round lengths to the nearest tenth.

Example 5 Solve a Triangle with Missing Angle

AnglesA =B =C =

Sidesa = b =c =

Solve triangle ABC. Round lengths to the nearest tenth.

5

A B

C

12

Example 6 Angle of Elevation and Depression

Line of Sight

Line of Sight

Depression of Angle

Elevation of Angle