Download Exam 2F

McKeague/Turner - Trigonometry 6e - Chap 2, Form F
Multiple Choice
____
1. Find tan B in the right triangle below.
a.
b.
c.
d.
e.
____
2. Simplify the following expression by first substituting values from the table of exact values and then
simplifying the resulting expression.
Table of Exact Values
x
sin x
0
1
a.
b.
c.
d.
e.
cos x
1
0
6
3
4
5
7
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
____
3. For expression 14cos (z - 30°), replace z with 60°, and then simplify as much as possible.
a.
b.
c.
d.
e.
____
4. Find the exact value for
.
a.
b. 0
c.
d.
e.
____
5. Find the exact value of tan 45°.
a.
b.
c.
d.
e.
5
1
-2
3
2
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
____
6. Suppose each edge of the cube shown in the figure is 4 inches long. Find the sine and cosine of the angle
formed by diagonals GB and GD.
a.
b.
c.
d.
e.
____
7. Use a calculator to find a value of between and
that satisfies the statement below. Write your
answer in degrees and minutes rounded to the nearest minute.
a.
b.
c.
d.
e.
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
____
8. Calculate the tangent values for each value of x indicated in the sets of tables shown below. Determine
which set of tables displays the correct values. Round all answers to the nearest tenth.
a. X
X
b. X
X
tan
15.9
19.1
23.9
31.8
47.7
95.5
undefined
tan
47.7
57.3
71.6
95.5
143.2
286.5
undefined
c. X
tan
15.9
19.1
23.9
31.8
47.7
95.5
undefined
tan
47.7
57.3
71.6
95.5
144.2
286.5
undefined
d. X
X
X
tan
15.9
19.1
23.9
31.8
47.7
95.5
undefined
tan
47.7
57.3
71.6
95.5
139.2
286.5
undefined
tan
15.9
19.1
23.9
31.8
47.7
95.5
undefined
tan
47.7
57.3
71.6
95.5
145.2
286.5
undefined
122
e. X
X
tan
15.9
19.1
23.9
31.8
47.7
95.5
undefined
tan
47.7
57.3
71.6
95.5
146.2
286.5
undefined
McKeague/Turner - Trigonometry 6e - Chap 2, Form F
____
9. Refer to right triangle ABC with C = 90 .
If B = 16.5 and c = 7.35 cm, find b.
Round the answer to the nearest hundredth.
a.
b.
c.
d.
e.
2.09 cm
1.97 cm
2.12 cm
2.18 cm
2.15 cm
____ 10. Refer to right triangle ABC with C = 90 .
If b = 9.5 mm and c = 13 mm, find B.
Round the answer to the nearest whole number.
a.
b.
c.
d.
e.
47
48
49
51
50
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
____ 11. The circle in the figure has a radius of r and center at C. The distance from A to B is x.
If A = 31 and r = 12, find x.
Round the answer to the nearest whole number.
a.
b.
c.
d.
e.
14
13
11
7
10
____ 12. The figure shows a simplified model of the first Ferris wheel. The radius of the first Ferris wheel was 125
feet, and the distance from the ground to the bottom of the wheel was 14 feet. If is the central angle
formed as a rider moves from position
to position
, find the rider's height above the ground h when
is 315 .
Round the answer to the nearest whole number.
a.
b.
c.
d.
e.
51 ft
39 ft
55 ft
45 ft
54 ft
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
____ 13. Solve the problem. Be sure to make a diagram of the situation with all the given information labeled.
A tree on one side of a river is due west of a rock on the other side of the river. From a stake 21 yards
north of the rock, the bearing of the tree is
. How far is it from the rock to the tree?
a.
b.
c.
d.
e.
9.4 yd
8.0 yd
7.0 yd
8.5 yd
1.7 yd
____ 14. Suppose the figure below is an exaggerated diagram of a plane flying above the earth. If the plane is 4.25
miles above the earth and the radius of the earth is 4,000 miles, how far is it from the plane to the
horizon? Round your answer to the nearest mile.
a.
b.
c.
d.
e.
183 mi
184 mi
174 mi
187 mi
199 mi
____ 15. A bullet is fired into the air with an initial velocity of 1,600 feet per second at an angle of
horizontal. Find the horizontal and vertical vector components of the velocity.
a.
b.
c.
d.
e.
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from the
McKeague/Turner - Trigonometry 6e - Chap 2, Form F
Numeric Response
16. Change the following to decimal degrees. If rounding is necessary, round to the nearest hundredth of a
degree.
__________
17. Refer to right triangle ABC with C = 90 .
If a = 42.9 inches and b = 32.3 inches, find B.
Apply the rules regarding the use of significant digits when determining your answer.
B = __________
18. Solve the following problem. Be sure to make a diagram of the situation with all the given information
labeled.
A person standing on top of a 12-foot high sand pile wishes to estimate the width of the pile. He visually
locates two rocks on the ground below at the base of the sand pile. The rocks are on opposite sides of the
sand pile, and he and the two rocks are in line with one another. If the angles of depression from the top
of the sand pile to each of the rocks are
and
, how far apart are the rocks?
Apply the rules regarding the use of significant digits when determining your answer.
Distance between rocks = __________ ft
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
19. The magnitude of the horizontal and vertical vector components
and
of vector V are given. Find
the magnitude of V. Apply the rules regarding the use of significant digits when determining your
answers.
= __________
20. Mark pulls Allison and Mattie in a wagon by exerting a force of 20 pounds on the handle at an angle of
with the horizontal. How much work is done by Mark in pulling the wagon 330 feet? Apply the rules
regarding the use of significant digits when determining your answer.
__________
Short Answer
21. Find the exact value for
.
22. Use a calculator to find a value of between and
that satisfies the statement below. Write your
answer in degrees and minutes rounded to the nearest minute.
_____ _____'
23. Refer to right triangle ABC with C = 90 . Solve for all the missing parts using the given information.
m
Apply the rules regarding the use of significant digits when determining your answer.
B = __________
a = __________ m
b = __________ m
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
24. A ship travels 185 kilometers on a bearing of
.
Apply the rules regarding the use of significant digits when determining your answers.
How far east has it traveled?
__________ km
How far south has it traveled?
__________ km
25. A 10-pound weight is lying on a sit-up bench at the gym. If the bench is inclined at an angle of
, there
are three forces acting on the weight. N is called the normal force and it acts in the direction perpendicular
to the bench. F is the force due to friction that holds the weight on the bench. If the weight does not move,
then the sum of these three forces is 0.
Find the magnitude of N and the magnitude of F. Apply the rules regarding the use of significant digits
when determining your answers.
| N | = __________ lb
| F | = __________ lb
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McKeague/Turner - Trigonometry 6e - Chap 2, Form F
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
A
B
B
C
B
A
D
A
A
A
C
A
C
B
D
NUMERIC RESPONSE
16.
17.
18.
19.
20.
45.55
37.0
56
47.8
5,100
SHORT ANSWER
21.
22.
23.
24.
25.
;
;
;
;
;
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