Download Geo - CH8 Practice Test

Geo - CH8 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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1. Write a similarity statement comparing the three triangles in the diagram.
a. ΔGFJ ∼ ΔGHF ∼ ΔJHF
c. ΔGFJ ∼ ΔFHG ∼ ΔFJH
b. ΔGFJ ∼ ΔGFH ∼ JFH
d. ΔGFJ ∼ ΔGHF ∼ ΔFHJ
2. Use your calculator to find trigonometric ratios sin 79°, cos 47°, and tan 77°. Round to the nearest
hundredth.
a. sin 79° = –0.99, cos 47° = –0.44, tan 77° = –32.27
b. sin 79° = –0.44, cos 47° = –0.99, tan 77° = –32.27
c. sin 79°= 0.68, cos 47° = 0.98, tan 77° = 4.33
d. sin 79° = 0.98, cos 47° = 0.68, tan 77° = 4.33
3. Jessie is building a ramp for loading motorcycles onto a trailer. The trailer is 2.8 feet off of the
ground. To avoid making it too difficult to push a motorcycle up the ramp, Jessie decides to make
the angle between the ramp and the ground 15°. To the nearest hundredth of a foot, find the length
of the ramp.
a. 10.82 feet
c. 0.72 feet
b. 2.90 feet
d. 10.45 feet
−1
−1
−1
4. Use your calculator to find the angle measures sin (0.7), cos (0.3), and tan (38.4)to the nearest
tenth of a degree.
a. sin−1(0.7) = 44.4º, cos−1(0.3) = 72.5º, tan−1(38.4) = 88.5º
b. sin−1(0.7) = 0.8º, cos−1(0.3) = 1.3º, tan−1(38.4) = 1.5º
c. sin−1(0.7) = 1.3º, cos−1(0.3) = 0.8º, tan−1(38.4) = 1.5º
d. sin−1(0.7) = 72.5º, cos−1(0.3) = 44.4º, tan−1(38.4) = 88.5º
5. Some mountains in the Alps are very steep and have a grade of 42.7%. To the nearest degree, what
angle do these mountains make with a horizontal line?
a. 23°
c. 47°
°
b. 67
d. 32°
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6. The largest Egyptian pyramid is 146.5 m high. When Rowena stands far away from the pyramid,
her line of sight to the top of the pyramid forms an angle of elevation of 20° with the ground. What
is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest
meter.
a. 402 m
c. 156 m
b. 427 m
d. 65 m
7. An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15°.
What is the horizontal distance between the eagle and its prey? Round to the nearest foot.
a. 1,120 ft
c. 310 ft
b. 1,159 ft
d. 723 ft
8. Use a calculator to find the trigonometric ratios sin 123°, cos 95°, and tan 125°. Round to the
nearest hundredth.
a. sin 123° = –0.09, cos 95° = 0.84, tan 125° = –1.43
b. sin 123° = –0.46, cos 95° = 0.73, tan 125° = –0.78
c. sin 123° = 0.84, cos 95° = –0.09, tan 125° = –1.43
d. sin 123° = 0.84, cos 95° = 0.996194698092, tan 125° = –1.43

→
9. Write the vector AB in component form.
a.
b.
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〈 5, − 3 〉
〈 −3, 5 〉
c.
d.
〈 −5, 3 〉
〈 3, − 5 〉
10. Sketch a 160° angle on the coordinate plane. Find the measure of its reference angle.
a. Reference angle: 110°
c. Reference angle: 340°
b. Reference angle: 20°
d. Reference angle: 70°
Numeric Response
11. A hiking trail has a slope of 327 . What is the measure of the angle that the trail makes with a
horizontal line? Round to the nearest degree.
12. Mike and Lani stand 21.2 meters apart. From Mike’s position, the angle of elevation to the top of
the Eiffel Tower is 40°. From Lani’s position, the angle of elevation to the top of the Eiffel Tower
is 38.5°. How many meters high is the Eiffel Tower? Round to the nearest meter.

→

→
13. TM has an initial point of (−5, 5) and a terminal point of (−7, − 3). Find the magnitude of TM to
the nearest tenth.
Matching
Match each vocabulary term with its definition.
a. cosine
b. adjacent leg
c. sine
d. tangent
e. trigonometric ratio
f. angle of depression
g. opposite leg
h. angle of elevation
i. geometric mean
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14. the angle formed by a horizontal line and a line of sight to a point above
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15. for positive numbers a and b, the positive number x such that a = x
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x
b
16. in a right triangle, the ratio of the length of the leg opposite the angle to the length of the
hypotenuse
17. in a right triangle, the ratio of the length of the leg adjacent to the angle to the length of the
hypotenuse
18. in a right triangle, the ratio of the length of the leg opposite the angle to the length of the leg
adjacent to the angle
19. a ratio of two sides of a right triangle
Match each vocabulary term with its definition.
a. parallel vectors
b. resultant vector
c. additive vector
d. direction
e. equal vectors
f. magnitude
g. multiplicative vector
h. component form
i. vector
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20. a quantity that has both magnitude and direction
21. two vectors that have the same magnitude and the same direction
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22. the length of a vector, written AB or v
| | | |
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23. the orientation of a vector, which is determined by the angle the vector makes with a horizontal
line
| → |
| → |
Geo - CH8 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: D
Sketch the three right triangles with the angles of the triangles in corresponding positions.
The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other
and to the original triangle, so ΔGFJ ∼ ΔGHF ∼ ΔFHJ.
Feedback
A
B
C
D
All corresponding long legs must match up.
All right angles must align.
Sketch the triangles in similar orientations to help you align corresponding parts.
Correct!
PTS: 1
DIF: Average
REF: Page 518
OBJ: 8-1.1 Identifying Similar Right Triangles
TOP: 8-1 Similarity in Right Triangles
2. ANS: D
Make sure your calculator is in degree mode.
sin 79° = 0.98, cos 47° = 0.68, tan 77° = 4.33
NAT: 12.3.2.e
Feedback
A
B
C
D
Change your calculator to degree mode.
Change your calculator to degree mode.
Switch the first and second answers.
Correct!
PTS:
OBJ:
TOP:
3. ANS:
1
DIF: Basic
REF: Page 526
8-2.3 Calculating Trigonometric Ratios
8-2 Trigonometric Ratios
A
NAT: 12.2.1.m
sin A = BC
AB
sin 15° = 2.8
AB
AB = 2.8
sin 15°
AB ≈ 10.82 feet
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by AB and divide by sin 15°.
Simplify the expression.
Feedback
A
B
C
D
Correct!
Since the hypotenuse and opposite side are involved, use the sine ratio.
The ramp should be substantially larger than the opposite leg, because the
opposite leg is across from the smallest possible angle in the triangle.
Draw a picture to help determine which trigonometric ratio to use.
PTS: 1
DIF: Average
REF: Page 528
OBJ: 8-2.5 Problem-Solving Application NAT: 12.2.1.m
TOP: 8-2 Trigonometric
Ratios
4. ANS: A
Change your calculator to degree mode.
Use the inverse trigonometric functions on your calculator to find each angle measure.
sin−1 ( 0.7 ) = 44.4°, cos−1 ( 0.3 ) = 72.5°, tan−1 ( 38.4 ) = 88.5°
Feedback
A
B
C
D
Correct!
Change your calculator to degree mode.
Change your calculator to degree mode.
Switch the first and second answer.
PTS:
OBJ:
NAT:
5. ANS:
1
DIF: Basic
REF: Page 535
8-3.2 Calculating Angle Measures from Trigonometric Ratios
12.2.1.m
TOP: 8-3 Solving Right Triangles
A
42.7% =
42.7
100
Change the percent grade to a fraction.
A 42.7% grade means the mountain rises 42.7 ft for every 100 ft of horizontal distance.
∠A is the angle the mountain makes with a horizontal line.
ˆ˜
m∠A = tan−1 ÊÁË 42.7
100 ¯ ≈ 23°
Feedback
A
B
C
D
Correct!
Find the complement of this angle.
Convert 42.7% to a fraction. Take the inverse tangent of this fraction.
Convert 42.7% to a fraction. Take the inverse tangent of this fraction.
PTS: 1
NAT: 12.2.1.m
6. ANS: A
tan 20° = 146.2
x
146.2
x=
tan 20°
x ≈ 402 m
DIF: Average
REF: Page 536
TOP: 8-3 Solving Right Triangles
OBJ: 8-3.5 Application
Use the side opposite ∠A and x, and the side adjacent to ∠A to
write the tangent ratio.
Multiply both sides by x and divide both sides by tan 20°.
Simplify.
Feedback
A
B
C
D
Correct!
Divide 146.2 by tan 20.
Divide 146.2 by tan 20.
Change your calculator to degree mode.
PTS:
OBJ:
TOP:
7. ANS:
1
DIF: Average
REF: Page 545
8-4.2 Finding Distance by Using Angle of Elevation
8-4 Angles of Elevation and Depression
A
NAT: 12.2.1.k
By the Alternate Interior Angles Theorem, m∠S = 15°. From the sketch, tan 15° = 300 . So
x
x = 300 ≈ 1, 120 ft.
tan 15°
Feedback
A
B
C
D
Correct!
Divide 300 by tan 15.
Divide 300 by tan 15.
Divide 300 by tan 15.
PTS: 1
DIF: Average
REF: Page 545
OBJ: 8-4.3 Finding Distance by Using Angle of Depression
NAT: 12.2.1.k
TOP: 8-4 Angles of Elevation and Depression
8. ANS: C
Change the calculator mode to degrees.sin 123° = 0.84, cos 95° = −0.09, tan 125° = −1.43
Feedback
A
B
C
D
The first question uses the sine function.
Change the calculator mode to degrees.
Correct!
The second question uses the cosine function.
PTS: 1
DIF: Basic
REF: Page 551
OBJ: 8-5.1 Finding Trigonometric Ratios for Obtuse Angles
TOP: 8-5 Law of Sines and Law of Cosines
9. ANS: A
The horizontal change from A to B is 5 units.
The vertical change from A to B is –3 units.

→
So the component of AB is
〈 5, − 3 〉.
Feedback
A
B
C
D
Correct!
The first number is the horizontal component.
The horizontal component is 5.
The first number is the horizontal component.
PTS:
1
DIF:
Average
REF: Page 559
OBJ: 8-6.1 Writing Vectors in Component Form
TOP: 8-6 Vectors
10. ANS: B
NAT: 12.3.4.e
The reference angle is the acute angle formed between the ray shown in the sketch, and the
negative x-axis. That angle is 180° − 160° = 20°.
Feedback
A
B
C
D
The reference angle is an acute angle.
Correct!
The reference angle is an acute angle.
The x-axis (not the y-axis) is one side of a reference angle.
PTS: 1
DIF: Basic
OBJ: 8-Ext.1 Finding Reference Angles
KEY: unit circle | reference angle
REF: Page 570
TOP: 8-Ext Trigonometry and the Unit Circle
NUMERIC RESPONSE
11. ANS: 12
PTS: 1
DIF: Basic
TOP: 8-3 Solving Right Triangles
12. ANS: 324
NAT: 12.2.1.m
PTS: 1
DIF: Advanced
NAT: 12.2.1.m
TOP: 8-4 Angles of Elevation and Depression
13. ANS: 8.2
PTS:
1
DIF:
Advanced
TOP: 8-6 Vectors
14. ANS: H
PTS:
1
DIF:
MATCHING
Basic
REF: Page 544
15.
16.
17.
18.
19.
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
20. ANS:
TOP:
21. ANS:
TOP:
22. ANS:
TOP:
23. ANS:
TOP:
8-4 Angles of Elevation and Depression
I
PTS: 1
DIF:
8-1 Similarity in Right Triangles
C
PTS: 1
DIF:
8-2 Trigonometric Ratios
A
PTS: 1
DIF:
8-2 Trigonometric Ratios
D
PTS: 1
DIF:
8-2 Trigonometric Ratios
E
PTS: 1
DIF:
8-2 Trigonometric Ratios
I
8-6 Vectors
E
8-6 Vectors
F
8-6 Vectors
D
8-6 Vectors
Basic
REF: Page 519
Basic
REF: Page 525
Basic
REF: Page 525
Basic
REF: Page 525
Basic
REF: Page 525
PTS:
1
DIF:
Basic
REF: Page 559
PTS:
1
DIF:
Basic
REF: Page 561
PTS:
1
DIF:
Basic
REF: Page 560
PTS:
1
DIF:
Basic
REF: Page 560