Pearson 8 5 Form G – Fill Out and Use This PDF

Practice A

LESSON

8-5

Law of Sines and Law of Cosines

1.

sin 168

2.

cos 147

3.

tan 107

4.

sin 97

5.

cos 94

6. tan 140

7.

sin 121

8.

cos 170

9.

tan 135

b 2 a 2 c 2 2ac

, and

a 2 b 2 2ab cos C.

12.

#

20 m

%

13. 0

6.2 cm

2

47°

109°

3.5 cm

70°

$

1

sin D

sin C

sin Q

sin R

CE

DE

PR

PQ

DE

mR

14.

&

15.

-

7 ft

50°

5 cm

$ 39°

34° %

.

7 cm

,

EF

mN

Practice A

Practice B

LESSON

LESSON

8-5

Law of Sines and Law of Cosines

8-5

Law of Sines and Law of Cosines

Use a calculator to find each trigonometric ratio. Round to the nearest hundredth.

Use a calculator to find each trigonometric ratio. Round to the nearest hundredth.

1.

sin 168

0.21

2.

cos 147

0.84

3. tan 107

3.27

1.

sin 111

0.93

2.

cos 150

0.87

3.

tan 163

0.31

4.

sin 97

0.99

5.

cos 94

0.07

6. tan 140

0.84

4.

sin 92

1.00

5.

cos 129

0.63

6.

tan 99

6.31

7.

sin 121

0.86

8.

cos 170

0.98

9. tan 135

1.00

7.

sin 170

0.17

8. cos 96

0.10

9.

tan 117

1.96

Use the Law of Sines to find each measure. Round lengths to the nearest

10. For any ABC with side lengths a, b, and c, sin A

sin B

sin C.

tenth and angle measures to the nearest degree.

a

b

c

"

%

(

11. For any ABC with side lengths a, b, and c, a 2 b 2 c 2 2bc cos A,

10.

11.

12.

71°

c 2 a 2 b 2 2ab cos C.

b 2 a 2 c 2 2ac cos B , and

39 km

!

40°

25 m

#

& 45°

3.8 in.

63° $

) 116° 35° '

For Exercises 12 and 13, substitute numbers into the given Law of Sines ratio

BC 17.0 m

DE 2.8 in.

GH 61.1 km

to find each measure. Round lengths to the nearest tenth and angle measures

to the nearest degree.

12. #

47°

20 m

%

13.

0

6.2 cm

2

13. ,

YD

*

14.

0

15.

3

— MI

3.5 cm

16.9 ft

24.7 ft

109°

70°

YD

—

5

$

1

+

2

43°

MI

sin D sin C

sin Q

sin R

4

1

CE

DE

PR

PQ

mJ

55

mR

85

mT

18

15.5

32

DE

mR

Use the Law of Sines to find each measure. Round lengths to the nearest

Use the Law of Cosines to find each measure. Round lengths to the nearest

tenth and angle measures to the nearest degree.

tenth and angle measures to the nearest degree.

14.

&

15.

-

16.

4 ft

9

17. "

18.

&

50°

8

52°

$

7 ft

5 cm

3 cm

5.8 mi

39°

34°

2.3 cm

%

$

%

.

7 cm

,

7.6 ft

87°

112°

6.3 mi

:

#

'

EF

7.9 ft

mN

33

YZ

6.0 ft

BD 3.7 cm

EF 10.0 mi

For Exercises 16 and 17, substitute numbers into the Law of Cosines to find

35

19.

)

*

20.

20 ft

-

21.

3

8.8 yd

2

each measure. Round lengths to the nearest tenth and angle measures to the

nearest degree.

43

74.2

,

10 ft

9.4 yd

6.2 yd

3.2 in.

92.4°

15 ft

16. 3

58°

3.5 in. TU

17.

8 yd

'

mH

(

+

1

4.8 yd

4

3 in.

144

47

40

)

(

mI

mM

mS

5

6.2 yd

TU 2 ST 2 SU 2 2(ST )(SU )(cos S)

GI 2 GH 2 HI 2 2(GH )(HI )(cos H )

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35

Holt Geometry

All rights reserved.

36

Holt Geometry

Copyright © by Holt, Rinehart and Winston.

Copyright © by Holt, Rinehart and Winston.

Practice C

Review for Mastery

LESSON

LESSON

8-5

Law of Sines and Law of Cosines

8-5

Law of Sines and Law of Cosines

The figure shows a 30

angle and a 150

angle in a coordinate

i

Y

i

You can use a calculator to find trigonometric ratios for obtuse angles.

plane. Notice the special triangles that the angles make with the

—

sin 115

0.906307787

cos 270 0

tan 96 9.514364454

x-axis. The figure also shows the trigonometric ratios for each angle.

1. Sketch a 60 angle and a 120 angle in a coordinate plane.

—

—

X

The Law of Sines

Give the coordinates of the vertices of the special right

i

i

For any ABC with side lengths a, b, and c that

B

c

triangles that the angles make with the x-axis. Give the

are opposite angles A, B, and C, respectively,

A

hypotenuses a length of 1 unit.

a

SIN— n

SIN— n

sin A

sin B

sin C

b

j

j

COS—

i

COS—

i

.

a

c

C

Y

TAN—

i

TAN—

i

b

Find mP. Round to the nearest degree.

sin P

sin N

Law of Sines

M

MN

PM

7 in.

10 in.

sin P sin 36

X

MN 10, mN 36, PM 7

10 in.

7 in.

36°

N

sin P 10 in.sin7 in.36

P

3

;

1

;

3

Multiply both sides by 10 in.

2. Find the sine, cosine, and tangent of 60.

sin P

0.84

Simplify.

2

2

3. Find the sine, cosine, and tangent of 120.

3

;

1

;

3

mP

sin1 (0.84)

Use the inverse sine function to find mP.

2

2

mP

57

Simplify.

j

j

Use a calculator to find each trigonometric ratio. Round to the nearest

Y

j

j

hundredth.

1. cos 104

2. tan 225

3. sin 100

0.24

1

0.98

X

j

j

Find each measure. Round the length to the nearest tenth and the angle

measure to the nearest degree.

Give the hypotenuses a length of 1 unit.

2

;

2

; 1

4. TU

5. mE

5. Find the sine, cosine, and tangent of 45.

T

F

2

2

42 in.

2

;

2

;

1

18 m

26 in.

6. Find the sine, cosine, and tangent of 135.

2

2

64°

41°

102°

S

U

E

G

cosine of the angle’s complement, cos (90 A).

24.7 m

37

Possible answer: The sine of an angle is equal to the cosine of the angle’s

complement: sin A cos (90 A).

All rights reserved.

59

Holt Geometry

Copyright © by Holt, Rinehart and Winston.