13.1 – Use Trig with Right Triangles

Hypotenuse:

Opposite side:

Adjacent side:

Side opposite right angle

Hypotenuse

Side opposite reference angle

Op

pos

ite

Side next to reference angle, not hypotenuse

Adjacent

HypotenuseOp

pos

ite

Adjacent

sin = opphyp

cos = adjhyp

tan = oppadj

csc = hypopp

sec = hypadj

cot = adjopp

csc = 1 .

sin sec = 1 .

cos cot = 1 .

tan

csc = cosecant

sec = secant

cot = cotangent

SOH – CAH – TOA

1. Evaluate the six trigonometric functions of the angle .

sin = 915

cos = 1215

tan = 912

csc = 15 9

sec = 1512

cot = 12 9

c2 = a2 + b2

152 = a2 + 92

225 = a2 + 81144 = a2

12 = a12

H

A

O

2. Let be an acute angle of a right triangle. Find the value of the other five trigonometric functions of .

4sin

5

4 5

c2 = a2 + b2

52 = a2 + 42

25 = a2 + 169 = a2

3 = a

sin = 45

cos = 35

tan = 43

csc = 54

sec = 53

cot = 34

3

H

A

O

2. Let be an acute angle of a right triangle. Find the value of the other five trigonometric functions of .

21

c2 = a2 + b2

c2 = 1 + 3c2 = 4c = 2

sin = 45

cos = 35

tan = 43

csc = 54

sec = 53

cot = 34

cot 3

3

cot = adjopp

22 21 3c H

A

O

3. Find the measure of the missing sides. Round to the nearest hundredth.

c dH

A

Osin 42° =

c7

7 sin 42° = c

1

4.68 = c

cos 42° =d7

7 cos 42° = d

1

5.20 = d

SOH – CAH – TOA

3. Find the measure of the missing sides. Round to the nearest hundredth.

a b

tan 57° = 14 a

a tan 57° = 14

1

a = 9.09

sin 57° = 14 b

b sin 57° = 14

1

16.69 = b

H

O

A

SOH – CAH – TOA

4. Solve ABC, using the diagram and the given measurements.

A = 40°, c = 8 A

B

C

a

b

c

40° 8H

O

A 50°

40°

90°

8

a b

sin 40° = a8

8 sin 40° = a

1

a = 5.14

cos 40° = b8

8 cos 40° = b

1

6.13 = b

SOH – CAH – TOA

5.14

6.13

Remember special triangles?

45° 45° 90°

1 1 2

1

1

2

30° 60° 90°

1 23

21

345°

45° 60°

30°

5. Find the exact values of the variables.

1

1

2 x = 13

y = 13 2

5. Find the exact values of the variables.

x =

14y =

7 3

2

13

60°

2

1

3

5. Find the exact values of the variables.

x = 3

y = 3 3

5. Find the exact values of the variables.

2

1

3

x = 18

3

3

3

18 3

36 3

y = 12 3