Chapter 8 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. In triangle ABC,
is a right angle and
simplest radical form.
45. Find BC. If you answer is not an integer, leave it in
C
11 ft
B
A
Not drawn to scale
a. 22 ft
____
b. 22
ft
c. 11 ft
d. 11
c. 5
d. 18
ft
2. Find the length of the hypotenuse.
45°
3 2
a. 12
____
b. 6
3. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
16
45°
Not drawn to scale
a. 128
____
b. 8 2
c. 16
d. 2 2
4. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to
the nearest tenth.
y
7
45°
x
Not drawn to scale
a. x = 7, y = 9.9
____
b. x = 9.9, y = 7
c. x = 4.9, y = 6.1
d. x = 6.1, y = 4.9
5. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
45°
x
5
Not drawn to scale
a.
b.
c.
d.
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
____
6.
6
x
60°
12
Not drawn to scale
a. 2
____
b.
c.
1
2
7.
x
y
30°
20
Not drawn to scale
a. x =
,y=
b. x = 10, y =
c. x =
, y = 10
d. x = 30, y =
d.
____
8.
y
17
30°
x
Not drawn to scale
a. x = 17, y =
b. x = 34, y =
____
c. x =
d. x =
, y = 17
, y = 34
9. Find the value of x and y rounded to the nearest tenth.
x
34
45°
30°
y
a. x = 48.1, y = 46.4
b. x = 48.1, y = 139.3
c. x = 24.0, y = 139.3
d. x = 24.0, y = 46.4
____ 10. Write the tangent ratios for
and
.
P
29
21
R
Q
20
Not drawn to scale
a.
c.
b.
d.
____ 11. Write the tangent ratios for
Z
85
7
X
6
Y
Not drawn to scale
and
.
a.
c.
b.
d.
Find the value of x. Round your answer to the nearest tenth.
____ 12.

x
9
Not drawn to scale
a. 3.3
____ 13.
b. 3.1
c. 24.7
d. 8.5
b. 12.7 cm
c. 15.5 cm
d. 10.9 cm
c. 70
d. 85
c. 83
d. 53
8.9 cm
x

a. 6.2 cm
Find the value of x to the nearest degree.
____ 14.
19
11
x
Not drawn to scale
a. 30
b. 60
____ 15.
58
3
x
a. 67
b. 23
____ 16. The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to
the top of a building. They also measured their distance from the bottom of the building. The diagram shows
the angle measure and the distance. To the nearest foot, find the height of the building.
Building

100 ft
a. 2400 ft
b. 72 ft
c. 308 ft
d. 33 ft
____ 17. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts
a 249-foot-long shadow. Find the measure of
to the nearest degree.
100 ft
A
249 ft
a. 68
b. 45
c. 35
d. 22
c. 49.4
d. 67.4
____ 18. Find the missing value to the nearest tenth.
= 45
tan
a. 88.7
b. 77.4
____ 19. Write the ratios for sin A and cos A.
A
5
4
C
3
B
Not drawn to scale
a.
c.
b.
d.
____ 20. Write the ratios for sin X and cos X.
X
12
5
Z
Y
119
a.
c.
b.
d.
Find the value of x. Round to the nearest tenth.
____ 21.
x

11
Not drawn to scale
a. 12.5
b. 10
c. 13
d. 9.7
c. 12.4
d. 8.1
c. 10.7
d. 31.8
____ 22.
10

x
Not drawn to scale
a. 12.9
b. 8.5
____ 23.
18
x

Not drawn to scale
a. 10.3
b. 31.4
____ 24.
18
x

Not drawn to scale
a. 52.6
b. 52.9
c. 6.2
d. 6.5
Find the value of x. Round to the nearest degree.
____ 25.
9
18
x
Not drawn to scale
a. 60
b. 27
c. 26
d. 30
c. 46
d. 44
____ 26.
21
x
15
Not drawn to scale
a. 41
b. 36
____ 27. A slide 4.1 meters long makes an angle of 35 with the ground. To the nearest tenth of a meter, how far above
the ground is the top of the slide?
4.1 m
x

a. 7.1 m
b. 3.4 m
c. 5.0 m
d. 2.4 m
____ 28. Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.
10
11
w

x
a. w = 7.7, x = 44
b. w = 6.4, x = 54
c. w = 7.7, x = 54
d. w = 6.4, x = 44
Find the value of x. Round the length to the nearest tenth.
____ 29.
x

11 cm
Not drawn to scale
a. 7.1 cm
b. 13.1 cm
c. 9.2 cm
d. 8.4 cm
c. 8.6 m
d. 12.3 m
c. 15.3 ft
d. 7.9 ft
____ 30.
15 m
x

Not drawn to scale
a. 26.2 m
b. 10.5 m
____ 31.
11 ft

x
Not drawn to scale
a. 7.6 ft
b. 10.6 ft
____ 32.

x
200 m
Not drawn to scale
a. 1134.3 m
b. 1151.8 m
____ 33.
c. 34.7 m
d. 203.1 m
c. 9 yd
d. 31.2 yd

x
18 yd
Not drawn to scale
a. 15.6 yd
b. 10.4 yd
____ 34. An airplane over the Pacific sights an atoll at an angle of depression of 5 . At this time, the horizontal
distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?

x
4629 m
Not drawn to scale
a. 403 m
b. 405 m
c. 4611 m
d. 4647 m
____ 35. To approach the runway, a small plane must begin a 9 descent starting from a height of 1125 feet above the
ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this
approach?

1125 ft
x
Not drawn to scale
a. 1.3 mi
b. 1.4 mi
c. 0.2 mi
d. 7,191.5 mi
____ 36. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit
4 feet tall, measures the angle of elevation to the top of the pole to be 44 . To the nearest foot, what is the
height of the pole?
a. 145 ft
b. 149 ft
c. 135 ft
d. 139 ft
____ 37. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an
entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight
to the entrance door?
a. 39
b. 51
c. 53
d. 37
____ 38. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts
a shadow 14 yards long. Round to the nearest degree.
a. 54
b. 36
c. 46
d. 44
Short Answer
39. The diagram shows the locations of John and Mark in relationship to the top of a tall building labeled A.
A
3
1 2
ground level
a.
b.
Describe
Describe
4
Mark
5
John
as it relates to the situation.
as it relates to the situation.
40. A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12 .
Draw a diagram to represent this situation.
a.
To the nearest foot, how far is the fire from the base of the tower? Show the steps you
b.
use to find the solution.
Chapter 8 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
TOP:
2. ANS:
OBJ:
TOP:
3. ANS:
OBJ:
TOP:
4. ANS:
OBJ:
TOP:
5. ANS:
OBJ:
TOP:
6. ANS:
OBJ:
TOP:
7. ANS:
OBJ:
TOP:
8. ANS:
OBJ:
TOP:
9. ANS:
OBJ:
TOP:
10. ANS:
OBJ:
TOP:
KEY:
11. ANS:
OBJ:
TOP:
KEY:
12. ANS:
OBJ:
TOP:
13. ANS:
OBJ:
TOP:
14. ANS:
OBJ:
TOP:
D
PTS: 1
DIF: L3
REF: 8-2 Special Right Triangles
8-2.1 45°-45°-90° Triangles
STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 1
KEY: special right triangles
B
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.1 45°-45°-90° Triangles
STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 1
KEY: special right triangles | hypotenuse
B
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.1 45°-45°-90° Triangles
STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 2
KEY: special right triangles | hypotenuse | leg
B
PTS: 1
DIF: L3
REF: 8-2 Special Right Triangles
8-2.1 45°-45°-90° Triangles
STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 2
KEY: special right triangles | hypotenuse | leg
C
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.1 45°-45°-90° Triangles
STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 2
KEY: special right triangles | hypotenuse | leg
D
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.2 Using 30°-60°-90° Triangles STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 4
KEY: special right triangles | leg | hypotenuse
D
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.2 Using 30°-60°-90° Triangles STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 4
KEY: special right triangles | leg | hypotenuse
D
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.2 Using 30°-60°-90° Triangles STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 4
KEY: special right triangles | leg | hypotenuse
D
PTS: 1
DIF: L3
REF: 8-2 Special Right Triangles
8-2.2 Using 30°-60°-90° Triangles STA: CA GEOM 15.0| CA GEOM 20.0
8-2 Example 4
KEY: special right triangles | leg | hypotenuse
B
PTS: 1
DIF: L2
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 1
tangent ratio | tangent | leg opposite angle | leg adjacent to angle
C
PTS: 1
DIF: L3
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 1
leg adjacent to angle | leg opposite angle | tangent | tangent ratio
C
PTS: 1
DIF: L2
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 2
KEY: side length using tangent | tangent | tangent ratio
A
PTS: 1
DIF: L3
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 2
KEY: side length using tangent | tangent | tangent ratio
B
PTS: 1
DIF: L2
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 3
KEY:
15. ANS:
OBJ:
TOP:
KEY:
16. ANS:
OBJ:
TOP:
KEY:
17. ANS:
OBJ:
TOP:
KEY:
ratio
18. ANS:
OBJ:
TOP:
19. ANS:
OBJ:
TOP:
20. ANS:
OBJ:
TOP:
21. ANS:
OBJ:
TOP:
22. ANS:
OBJ:
TOP:
23. ANS:
OBJ:
TOP:
24. ANS:
OBJ:
TOP:
25. ANS:
OBJ:
TOP:
KEY:
26. ANS:
OBJ:
TOP:
KEY:
27. ANS:
OBJ:
TOP:
KEY:
28. ANS:
OBJ:
inverse of tangent | tangent | tangent ratio | angle measure using tangent
B
PTS: 1
DIF: L3
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 3
inverse of tangent | tangent | tangent ratio | angle measure using tangent
C
PTS: 1
DIF: L2
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 2
problem solving | word problem | tangent | side length using tangent | tangent ratio
D
PTS: 1
DIF: L3
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 3
angle measure using tangent | word problem | problem solving | tangent | inverse of tangent | tangent
A
PTS: 1
DIF: L3
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles STA: CA GEOM 18.0| CA GEOM 19.0
8-3 Example 3
KEY: angle measure using tangent
A
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 1
KEY: sine | cosine | sine ratio | cosine ratio
C
PTS: 1
DIF: L3
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 1
KEY: cosine | sine | sine ratio | cosine ratio
A
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 2
KEY: cosine | side length using since and cosine | cosine ratio
D
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 2
KEY: cosine | side length using since and cosine | cosine ratio
B
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 2
KEY: sine | side length using since and cosine | sine ratio
C
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 2
KEY: sine | side length using since and cosine | sine ratio
D
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 3
inverse of cosine and sine | angle measure using sine and cosine | sine
D
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 3
inverse of cosine and sine | angle measure using sine and cosine | cosine
D
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
8-4 Example 2
side length using since and cosine | word problem | problem solving | sine | sine ratio
A
PTS: 1
DIF: L3
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
STA: CA GEOM 18.0| CA GEOM 19.0
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
KEY: side length using since and cosine | angle measure using sine and cosine | problem solving | sine |
inverse of cosine and sine | sine ratio
ANS: C
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 2
KEY: tangent | side length using tangent | tangent ratio
ANS: C
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 2
KEY: sine | side length using since and cosine | sine ratio
ANS: D
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 2
KEY: cosine | side length using since and cosine | cosine ratio
ANS: B
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 3
KEY: sine | side length using since and cosine | sine ratio | angles of elevation and depression
ANS: B
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 3
KEY: tangent | side length using tangent | tangent ratio | angles of elevation and depression
ANS: B
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 2
KEY: side length using tangent | word problem | problem solving | tangent | angles of elevation and
depression | tangent ratio
ANS: B
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 3
KEY: side length using since and cosine | word problem | problem solving | sine | angles of elevation and
depression | sine ratio
ANS: D
PTS: 1
DIF: L3
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 2
KEY: side length using tangent | word problem | problem solving | tangent | angles of elevation and
depression | tangent ratio
ANS: A
PTS: 1
DIF: L3
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
KEY: angle measure using tangent | word problem | angles of elevation and depression | problem solving |
tangent | inverse of tangent | tangent ratio
ANS: B
PTS: 1
DIF: L3
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
KEY: angle measure using tangent | word problem | angles of elevation and depression | problem solving |
inverse of tangent | tangent ratio
SHORT ANSWER
39. ANS:
a.
b.
PTS:
OBJ:
TOP:
KEY:
40. ANS:
a.
is the angle of elevation from Mark to the top of the building labeled A.
is the angle of depression from the top of the building labeled A to John.
1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
8-5 Example 1
angles of elevation and depression | multi-part question | word problem
Ranger

21 ft
x
b.
=
x =
Fire
Use the tangent ratio.
Solve for x.
x
99
The fire is about 99 feet from the base of the tower.
PTS: 1
DIF: L3
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
STA: CA GEOM 18.0| CA GEOM 19.0
TOP: 8-5 Example 2
KEY: side length using tangent | word problem | multi-part question | problem solving | tangent | angles of
elevation and depression | tangent ratio