Name: ____________________________Class: ___________ Date: ______________

Pre-Calc: 6.1 – 6.4 Review Worksheet

SHOW ALL WORK for credit on quiz and highlight your answers. No Ink.

Use the Law of Sines to solve if possible the triangle. If two solutions exist, find both.

Round your answers to the nearest integer.

1. 25 , 6.2, 4 2. 75 , 51.2, 33.7

sin 25 sin sin 75 s

4 6.2 51.2

B a b A a b

A

Check f

41

or

3

in

33.7

180 41 25 180 39 75

sin 25 sin114 sin 75 sin 6

2nd triangle: 180 41 139 Check for 2nd triangle: 180 39 141

139 25 180 , so 2 triangle

6

4 51.

s

9

114

482

66

9

B

c c

A B

C C

c c

2

2

2

2

139

. 141 75 180 , so only 1 triangle

180 139 25

sin 25 sin 6

.

43

1

16

A

C

cc

3. Use the Law of Sines to solve.

A tree stands on a hillside of slope 28 from the horizontal. From a point 75 feet down the hill,

the angle of elevation to the top of the tree is 45 . Find the height of the tree.

sin17 sin 45

7531.01 ft

hh

2 2 22 2 2

2 2 2 2 2

Use the Law of Cosines to solve the triangle. Round your answers to 2 decimal places.

4. 5, 8, 10 5. 110 , 4, 4

5 8 10cos 4 4 2 4 4 cos110

97.90 6.5

2 5 8

8 10 5 4 6.55cos cos

2 8 1

5

0

a b c B a c

C

C

A

b

b

A

2

29.69 35.

4

2

04

52.41 34. 6

4 6 5

9

.5

A A

B C

6. Use Law of Cosines to solve.

Two planes leave Raleigh-Durham Airport at approximately the same time. One is flying 425 miles

per hour at a bearing of 355 , and the other is flying 530 miles per hour at a bearing of 67 . Draw

a figure that gives a visual representation of the problem and determine the distance between the

planes after they have flown for 2 hours.

2 2 2850 1060 2 850 1060

1135.5 mile

cos72

sd

d

2 2

7. Find the component form and the magnitude of the vector

Initial point: 1, 5 ; terminal point: 15,

14, 4

2 53

9

15 1, 9 - 5

14 4 212

v

v

v

Find , , and . Then sketch the resultamt vector.

8. , 2 3

a b c

u v u v 2u 3v

u i j v i j

2 22 2

Find the magnitude and the direction angle of the vector . State angle directions as positive

9. 5 4 10. 3 3

4 3

38.

tan tan5 3

45 180

5 4 3 3 18

11. 4 7 12.

7

225

4 3

8 1

1 2

v

v i j v i j

v v

v i j v i j

2 22 2

7 1tan tan

4 8

60.3 180 7.1 360

119.7 352.9

64 7 5 658 1

v v

13. An airplane has an airspeed of 430 miles per hour at a bearing of 135 . The wind velocity is 35 miles

per hour in the direction of N 30 E. Find the resultant speed and direction of the a

22

irplane.

Airspeed: 430cos 45 , 430sin 45

304.1, 304.1

Wind: 35cos60 , 35sin 60

17.5, 30.3

Groundspeed: 304.1 17.5, 304.1 30.3 321.6, 273.8

3 4221. 2.4 mile6 273.8

273.8tan 40

321

s per hour

.6

u

u

w

w

u v

u w

.4 90 40. 13 44 9.

Find the dot product of and .

14. 6, 7 , 3, 9

45 2

15. 3 7 , 11 5

6 3 7 9 3 11 7 5

u v

u v u i j v i j

u v u v

Use the vectors 3, 4 and 2, 1 to find the indicated quantity. State whether the

result is a vector or a scalar.

16. 2 17.

2 6, 8 3 2 4 1 2

2 50 6, 8

The result is a scalar. The

6 3 8 4

re

2

u v

u u u u v

u u v

u u u

sult is a vector.

2 22 2

Find the angle between the vectors.

7 718. cos sin 19. 2 2, 4

4 4

5 5cos sin 2, 1

6 6

2 2 2 4 12 2, cos

2 22 2 4 2 1

3 1 4 4 8, cos

2 2 8 16 2 1 24 3

2 3 2 1

2 2 2 2cos

2

2

u i j u

v i j v

u

v

2 2 2 22 3 1

2 2 2

6 2 6 2

6 24 4 4cos41 1 3 1 1 1

2 2 4 4

165 165180

20. cos 45 sin 45

co

16

s300 sin

0.5

11

12

300

6 1050 45

u i j

v i j