Review Sheet #5
Completely solve each of the following triangles. Determine what information is given
(SAS, SSS, SSA, etc), and state the calculator-ready form for each variable as well as the numerical answer to the nearest tenth.
1.

20, b

35, c

50 2.

44.5 , B

13.5 , c

18.4
3. HIT , H

71 , T

62 , h

20.3
4.
  s

18, h

6
5.
7.
52 , b

24, a

32 6.

35.3 , p

12.3, o

16.7
10.

18, b

33, c

12
BIG , b

14.6 ,
 m g
8.

7.9
m
,

6,
Find the area of each of the following triangles to the nearest tenth:
9.
  b

14.6
cm c

19.6
cm b

8, C

40

11.

21.3 , x
 
11.7
in
Be able to do the following:
Define a vector quantity, scalar quantity, resultant vector, and equivalent vectors
Explain how vector addition differs from scalar addition.
12.
Find the magnitude and direction of the given vector when (8, 15) is the terminal point and the vector is in standard position.
13.
Find the magnitude and direction of the given vector when (-1, 5) is the initial point and
(3, 9) is the terminal point.
Find the magnitude and direction of the vector sum w of the given pair of vectors. u
14.
 u

15
 v v

10

130
 u
15.
 u

70
 v v

35 u
16.
 u
18.

40
 v v u

100

50

128
 u
17.
 u

25
 v v

18 v

150 and the angle between them measures 165

.

19. u

16.2
v

11.5
and the angle between them measures 39

.
20. u

24.8
v

31.3
and the angle between them measures 99

.
21.
In one minute a plane descending at a constant angle of depression of 12.4

travels 1600 meters along its line of flight. How much altitude has it lost?
22.
Jack, Jill, and Bob decide to go to Cedar Point to ride their 308 ft. high roller coaster, and they show up at different times. Jill is the first one in line and is 38.9 feet from the base of the 308 ft. peak of the roller coaster. Jack is in the back of the line, where the angle of elevation to the top is 20 degrees. How long is the line? What is the angle of elevation from Jill to the top of the coaster?
Jack Jill
23.
A plane is headed due south with airspeed of 192 mph. A wind from a direction of 78

is blowing at 23 mph. Find the groundspeed and the resulting course of the plane.
24.
A pilot’s airspeed is 168 mph on a heading of 58 
. A wind is blowing to the north at 27 mph. Find the groundspeed and the resulting course of the plane.
25.
Mrs. Brownlow parked her car on a hill with an incline of 8

and walked downhill to the trunk of her car in order to remove her groceries. While she was standing behind her 2000 pound car, her parking brake gave out. Mrs. Brownlow can push 280 pounds (under stress). Will she avoid being squished?
26.
You are going on a trip from Potsdam, New York to New York City. Unfortunately there was a huge chemical spill in the middle of the route, thus you have to take a detour. From
Potsdam you have to take highway 44, which runs due east. You have to go 559 miles on
Highway 44. Now you have to take Highway 56, which runs 55

west of north. You have to go 378 miles on this road to reach New York City. How much time would you have saved if you went straight from Potsdam to New York City? Assume that all routes allow you to go 60 mph.
ANSWERS:
1. A

18.2 , B

33.1 , C

128.7

2. a

15.2, b

5.1, C

122

3. I

47 , i

15.7, t

19.0
4. No Triangle is Formed.

5. B

36.2 , C

91.8 , c

40.6
6. Two Triangles are Formed:
O
O

51.7 , G

93.0 , g

21.3
 
G
  g '

6.0
7. No Triangle is Formed 8. Two Triangles are Formed:

A 80.0 , B

60.0 , a

A
9.2
'
 
B
  a '

3.2
9. K = 60.2 cm 2 10. K = 50.1 m 2
17. Two triangles are formed: K
1
= 68.9 in
2
, K
2
= 11.4 in
2
12. u

17,
 u

61.9

13. u

5.7,
 u
14. w

14.9,
 w
59 15. w

96.3,
45
 w

43.8

16. w

58.9,
 w

86.0

17. w

42.3,
 w

49.8

18. w

59.3,
 w
 u or v
19. w

26.2, 16.0
 from u or 23.0
 from v
20. w

36.8, 57.1
 from u or 41.9
 from v
21.
343.6 meters
22. The line is 807.2 feet long. The angle of elevation from Jill’s position is 82.8º.
23.
Groundspeed is 198 mph and course is 186.5º.
24.
Groundspeed is 183.7 mph and course is 50.8º.
25.
Since 278 lb is less than 280 lb, she will not get squished.
26.
You would have saved 10.1 hours.