Download Trigonometry (Bank of Test Questions)

Trigonometry (Bank of Test Questions)
1. An 18-foot ladder is leaning against the side of a building forming a right triangle. The angle formed by the
ladder and the ground is 60°. Which is closest to the distance, in feet, of the bottom of the ladder from the base
of the wall?
A. 9
B. 10.4
C. 12.7
D. 15.6
2. A diagonal of a square mirror is 10 inches long. What is the length, in inches, of each side of the mirror?
A. 5 inches
B.
C. 10 inches
inches
D.
inches
3. Workers at a botanical garden constructed a flower planter in the shape of a pentagon. The dimensions of
the planter are shown below.
What is the perimeter of the flower planter?
A.
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feet
B.
feet
C.
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feet
D.
feet
4. Malcolm fastened an 85-inch clothesline to two walls that are 84 inches apart on level ground, as shown
below. He fastened one end of the clothesline 55 inches above the ground on one wall, pulled the line tight,
and then fastened the other end higher on the second wall.
How many inches above the ground is the clothesline fastened to the other wall?
A. 13 inches
B. 56 inches
C. 65 inches
D. 68 inches
5. A right triangle is shown below.
Which statement is always true?
A.
B.
C.
D.
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6. Triangle JKL is similar to triangle PQR. The sine of angle L is
What is the sine of angle R?
A.
B.
C.
D.
7. If Arc BE in the coordinate system below is the arc of a circle with the center at the origin, what is the
length of
?
A. 2
B. 3
C. 4
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8. In triangle ABC with right angle C, the measure of angle A is 37 degrees, and the length of the hypotenuse
is 10. What is the length of
A. 6
B. 7.5
C. 7.9
D. 12.5
9. What is the length of
in Triangle ABC?
A. 3 units
B. 6 units
C. 9 units
D. 12 units
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11. Calvin wanted to determine the amount of change, in degrees, that occurred in the elevation of the sun
between 5:45 p.m. and 6:45 p.m. on April 5th. He decided to measure the length, in feet, of the shadow
cast on the ground by his 5'10" height at both times. His results are shown in the table below.
Based on Calvin’s results, which statement best describes the changes that occurred in the elevation of the
sun between the given times on April 5th?
A. The elevation of the sun decreased by 10.4 degrees.
B. The elevation of the sun decreased by 13.0 degrees.
C. The elevation of the sun decreased by 25.9 degrees.
D. The elevation of the sun decreased by 29.1 degrees.
12. If cos(45°) 0.7071, what is sin(45°)?
A.
B.
C.
D.
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13. A right triangle is shown below.
Which equation represents a trigonometric ratio for the triangle?
A.
B.
C.
D.
(sec = reciprocal of cos)
14. A gate is shown in the diagram. A wire brace is extended diagonally across the gate as shown.
What is the length of the wire, x?
A. 7 ft
B. 6 ft
C. 5 ft
D. 4 ft
15. An escalator in a department store rises 80 feet at a 32° angle. What is the distance, x, from the bottom of
the escalator to the top of the escalator, to the nearest foot?
A. 94 feet
B. 113 feet
C. 128 feet
D. 151 feet
16. In right CDF, m D 90º and m C 29º. The length of the hypotenuse is 10 centimeters. Using the table
below, what is the length of
A. 2.9 cm
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to two significant digits?
B. 4.8 cm
C. 5.5 cm
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D. 8.7 cm
17. Right triangle ABC is shown below with the dimensions given in inches (in.).
What is AB to the nearest tenth of an inch?
A. 7.8
B. 10.4
C. 11.9
D. 13.7
18. A rope tied from a tent pole to a stake in the ground forms a 55° angle with the ground. The pole is 3 feet
from the stake as shown below.
What is the length of the rope, to the nearest tenth of a foot?
A. 1.7 feet
B. 3.7 feet
C. 4.3 feet
D. 5.2 feet
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19. The diagonal of a square microchip is 0.141422 centimeters. Which measure, in square centimeters, is
closest to the area of the microchip?
A. 0.01
B. 0.02
C. 0.1
D. 1
21. George is building a rectangular gate. The dimensions of the gate are 6 feet high and 4 feet wide. He
wants to fasten a thin brace diagonally at the corners to keep the gate sturdy. Approximately, how long is
the brace?
A. 4.0 feet
B. 4.5 feet
C. 7.2 feet
D. 10 feet
22. A computer screen has a width of 15 inches and a height of 11 inches. Approximately what is the length
of the screen’s diagonal?
A. 10.2 inches
B. 13.0 inches
C. 18.6 inches
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23. A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what
is the height of the screen?
A. 4.0 inches
B. 11.7 inches
C. 16.0 inches
D. 24.2 inches
24. In right
and
If
what is the length of
A. 9.7
B. 17.3
C. 37.3
D. 38.6
25. The diagram below shows
with the dimensions given in millimeters (mm).
What is the sin(R)?
A.
B.
C.
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26. Juan’s house has a rectangular doorway that is 8 feet high and 3 feet wide. Which measurement is closest
to the length of the diagonal of the doorway?
A. 3.3
B. 7.4
C. 8.5
D. 11.0
27. What is the length of
in the figure below?
A. 8 units
B. 12 units
C. 14.4 units
D. 20.8 units
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28. What is the approximate value of x, in inches, in the triangle below?
A. 17.2
B. 21.0
C. 30.0
D. 42.8
29. Triangle ABC is shown.
Which of these statements about Triangle ABC is true?
A. The Pythagorean Theorem proves that
is a right triangle.
B. The converse of the Pythagorean Theorem proves that
C. The Triangle Inequality Theorem proves that
is not a right triangle.
D. The converse of the Triangle Inequality Theorem proves that
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is a right triangle.
is not a right triangle.
30. If
and
relation between a and b?
which equation best describes the
A.
B.
C.
D.
31. A highway entrance ramp rises 4 feet above a horizontal road over a distance of 16 feet, as shown below.
Which equation can be used to determine the angle formed by the horizontal road and the entrance ramp?
A.
B.
C.
D.
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32. Joe used the Pythagorean theorem to make sure the picture frame he made is a precise rectangle.
If Joe’s picture frame is a precise rectangle, how long is each diagonal in the rectangle above?
A. 14 inches
B. 20 inches
C. 28 inches
D. 34 inches
33. In
is a right angle. If
and
what is the length of
A. 20 cos 49°
B. 20 sin 49°
C. 20 tan 49°
D.
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34. Two planes leave the airport at exactly the same time and travel at the same average speed. One plane
travels due north and the other travels due east as shown on the grid.
How far apart are the planes after they have each traveled 700 miles?
A.
miles
B. 1,050 miles
C. 1,400 miles
D.
miles
35. A window at the top of a building is in the shape of an isosceles right triangle as shown in the figure.
Which expression represents h, the distance from the peak of the window to its base in feet?
A.
B.
C. 3
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36. The figure below shows
If
is an isosceles triangle, what is the approximate length of
A. 23
B. 32
C. 39
D. 46
37. Helen constructed the spiral design shown below using seven right triangles. Both legs of the smallest
triangle are 1 unit in length. The shorter leg of each of the remaining 6 triangles is 1 unit in length.
What is x, the unit length of the hypotenuse of the largest triangle Helen used in the design?
A.
B.
C.
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38. Which equation shows a correct relation for triangle RSQ?
A.
B.
C.
D.
39. The figure below shows right triangle ABC and isosceles triangle ADC.
Line segment BD is a straight line.
Which of the following statements are true?
I.
II.
III.
A. I only
B. I and III only
C. II and III only
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40. A triangle has sides of lengths 26 cm and 80 cm. The angle between these two given sides has a measure
of 30°. What is the area of this triangle in square centimeters?
A. 186
B. 520
C.
D. 1040
41. Right triangle ABC is shown below with the dimensions given in units.
What is the
?
A.
B.
C.
D.
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42. The figure below shows right triangle
where
Which equation is true?
A.
B.
C.
D.
43. Right triangle ABC is shown below with the dimensions given in units.
Which measurement is closest to BC in units?
A. 3.9
B. 4.4
C. 4.6
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44. A 12-foot-tall pole is tethered to the ground by a wire at point T.
Which expression could be used to determine the measure of the angle that the wire makes with the
ground?
A.
B.
C.
D.
45. A ladder leaning against a wall makes an angle of 55° with the ground. If
the foot of the ladder is 6.5 feet from the wall, what is the length of the
ladder to the nearest hundredth?
A. 3.73 ft
B. 7.94 ft
C. 9.28 ft
D. 11.33 ft
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47. Look at the isosceles right triangle below.
What is the length of
A.
cm
B.
cm
C.
cm
D.
cm
48. Which of the following equations could be used to find the value of x in the right triangle below?
A.
B.
C.
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49. In the figure below, triangle ABC is similar to DEF. What is the value of
Write your answer in simplified radical form.
50. Right triangle PQR is shown below with the dimensions given in units.
Which ratio has a value equal to ?
A.
B.
C.
D.
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51. Pentagon MNPQR is shown below.
What is the length of
A.
B.
C.
D.
52.
In a right triangle, if cos
then what is sin x?
A.
B.
C.
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53. Benjamin is putting a fence around a right triangular garden. He has
already used 12 ft of fencing for one side of the garden, which makes an
angle of 65° with the longest side of the garden. To the nearest
hundredth, how many feet of fencing will Benjamin need for the longest
side?
A. 28.39
B. 13.24
C. 10.88
D.
5.07
54. Triangle JKL is shown below.
Which ratio represents
A.
B.
C.
D.
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55. When Donelle stands at point R, he is 1000 feet from point S at the base of a cliff.
When he looks up at an angle of 20°, he sees a friend at the top of the mountain cliff at point T. Which
measurement is the closest to the height of the mountain cliff in feet?
A. 342
B. 364
C. 940
D. 2747
56. The wind has blown a tree so that it is growing at a 108° angle with the ground. The top of the tree is 75
ft. from the ground.
How tall is the tree?
A. 71.3 ft.
B. 75 ft.
C. 78.9 ft.
D. 93 ft.
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57. A wire is attached 35 feet above the ground to a telephone pole. The wire makes an angle of 45° with the
ground, as shown below.
What is the length of the wire?
A.
B.
feet
C.
feet
D.
58.
feet
feet
The current route used to travel by a vehicle between City A and City C through City B is shown on the coordinate
grid below. A new road is under construction that will provide a direct route between City A and City C.
If each grid unit represents 3 kilometers, which is closest to the difference in distance between the new
route and the old route from City A to City C?
A. 9.1 kilometers
B. 12.1 kilometers
C. 14.9 kilometers
D. 19.1 kilometers
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59. The entrance to the tent forms an isosceles right triangle as shown, and the support pole, modeled by
forms an altitude to the hypotenuse.
If
how tall is the pole, in feet?
A. 5
B. 6
C. 8
D. 10
60.
In a right triangle, if tan
then what is cos
A.
B.
C.
D.
61. Squares ACFG, BCDE, and ABJH have areas 144, 256, and 400 square units, respectively.
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What are the dimensions of triangle ABC?
A.
B.
C.
D.
62. Jeff walked 54 meters along a river bank and saw a dock directly opposite him on the other side of the
river. The river is 24 meters wide at the point where he saw the dock, as shown in the diagram below.
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Which measurement is closest to the distance, in meters, of Jeff’s starting point from the dock?
A. 30.0
B. 48.4
C. 59.1
D. 78.0
63. What is the length of the diagonal of a square if its side length is
A. 7 inches
B. 14 inches
C.
D.
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inches?
64. If
what is the value of x?
A.
B.
C.
D.
65. The length of the sides of a triangle are 5, 12, and 13 inches. Which statement is true about this triangle?
A. The area of this triangle is 60
B. It is an acute triangle
C. It is a right triangle
D. The perimeter of this triangle is 25 in.
66. A 90-foot escalator rises a vertical distance of 45 feet, as shown in the diagram below.
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What is the measure of the angle identified with a question mark in the diagram?
A. 30°
B. 45°
C. 60°
D. 90°
67. A guide wire for a palm tree makes a 32° angle with the ground and is staked 6 feet from the base of the
tree, as shown below.
What is the length, to the nearest tenth of a foot, of the guide wire from the ground to the palm tree?
A. 7.1 feet
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B. 8.5 feet
C. 9.6 feet
D. 11.3 feet
68. Julian is flying a kite attached to a 100-foot-long string. If the string is tied to the ground at an angle of
elevation of 40°, what is the approximate height of the kite from the ground?
A. 64 feet
B. 77 feet
C. 84 feet
D. 100 feet
69. A 12-foot metal pole is leaning against a house, as shown below.
The pole forms a 50° angle with the ground. How many feet, to the nearest tenth of a foot, is the base of
the pole from the house?
A. 6.0 feet
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B. 7.7 feet
C. 8.5 feet
D. 9.2 feet
70. In a right triangle, if tan
then what is cos x?
A.
B.
C. 1
D.
71. In a right triangle, which of the following is the definition of the cosine ratio?
A.
B.
C.
D.
72. The dimensions of the right triangle shown below are given in units.
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Which measurement is the closest to
A. 20.6°
B. 22.0°
C. 68.0°
D. 69.4°
73. An equilateral triangle ABC is shown in the figure below.
If the height of
is 30 centimeters, what is the length of a side of this triangle in centimeters?
A.
B. 15
C. 30
D.
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74. For which value of
is the statement
true?
A. 40°
B. 50°
C. 60°
D. 140°
75.
The diagonal of a square microchip is
the area of the microchip?
centimeters. Which measure, in square centimeters, is closest to
A.
B.
C.
D.
76. A sphere is cut by parallel Planes P and Q as shown below. Plane P passes through the center of the
sphere, and Plane Q is located a distance of the radius of the sphere above the center.
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What is the ratio of the area of the circular cross section formed by Plane P to the area of the cross section
formed by Plane Q?
A. 2 : 1
B.
C. 4 : 1
D. 4 : 3
77. A ladder leaning against a wall makes a 55-degree angle with the floor. If the top of the ladder is 8 feet
from the floor, which expression represents the length of the ladder in feet?
A. 8(sin 45°)
B. 8(cos 45°)
C.
D.
78. Tess is installing a support wire to the top of the tree in her yard. The angle the wire makes with a point
on the ground 10 feet from the base of the tree is 75 degrees. How tall is the tree?
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A. 13 feet
B. 27 feet
C. 37 feet
D. 65 feet
79. A right triangle is shown below with the dimensions given in units.
What is the value of x in units?
A. 6
B.
C.
D. 12
80. If the base of a ladder is 5 feet from a building, how long must the ladder be to reach a window in the
building that is 15 feet above the ground?
A. 10.0 feet
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B. 14.1 feet
C. 15.8 feet
D. 20.0 feet
81. In
Which ratio represents the tangent
A.
B.
C.
D.
84. A person stands 10 feet away from the base of a 300-foot office building.
Which equation could be used to find the angle of elevation?
A.
B.
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C.
D.
85. Right triangle ABC is shown.
What is the length of
A.
B.
C.
D.
86. Sue made a quilt pattern from 16 congruent pieces of cloth shaped like isosceles right triangles. She cut
the pieces so that the legs of each triangular piece are 6 inches long.
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Which measurement is closest to x, the length in inches, of the hypotenuse of each triangular piece of
cloth?
A. 3.5
B. 4.2
C. 8.5
D. 18.0
87. A streetlight stands perpendicular to the ground. Martin measured the shadow of the streetlight. The
distance between the base of the streetlight and the tip of the shadow is 15 feet. In terms of this situation,
what could the expression below represent?
A. the angle of elevation from the tip of the shadow to the top of the streetlight if the streetlight is
10 feet tall
B. the height of the streetlight if the angle of elevation from the tip of the shadow to the top of the
streetlight is 10 degrees
C. the angle of elevation from the tip of the shadow to the top of the streetlight if the distance between
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the tip of the shadow and the top of the streetlight is 10 feet
D. the distance between the tip of the shadow and the top of the streetlight if the angle of elevation
from the tip of the shadow to the top of the streetlight is 10 degrees
88. Josh was skiing down a slope where the angle of elevation was 14º. If the length of the slope was 1500
feet, what was the vertical drop of the slope?
A. 374.0 feet
B. 362.9 feet
C. 1455.4 feet
D. 6200.3 feet
89.
In a right triangle, if
, what is sin x?
A.
B.
C.
D.
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90. A rope is tied from the top of a flagpole to a stake on the ground, as
shown below.
Which equation can be used to determine the value of x?
A.
B.
C.
D.
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91. Which pair of trigonometric functions has the same value?
A.
B.
C.
D.
92. Spring Elementary School is having a door decorating contest. Mr. Xolo’s
students want to use decorative tape to put an X on their door. The X will
be so big that it touches each corner of the door. The door is 84 inches
tall by 35 inches wide.
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What is the amount of decorative tape, in inches, that the students will
need to make the X?
A. 91 inches
B. 119 inches
C. 182 inches
D. 238 inches
93. Which of the following are lengths of the sides of a 30°–60°–90° triangle?
A.
B. 3, 4, and 5 units
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C.
D.
94. The diagram below shows
and
Part A. Find and compare
Part B. Explain whether
and
and
in these triangles.
are similar.
Use words, numbers, and/or pictures to show your work.
95.
and
Which expression represents the length of the altitude from
Vertex A?
A.
B.
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C.
D.
96. A rectangular cake is 24 centimeters long, 11 centimeters wide, and 7 centimeters tall. The cake is cut
perpendicular to and diagonally across the bases, as shown below.
What is the perimeter, to the nearest centimeter, of the cross section formed by the cut?
A. 64 centimeters
B. 67 centimeters
C. 70 centimeters
D. 84 centimeters
97. Right triangle RST is shown below with the dimensions given in feet (ft).
Which is closest to the measure of
?
A. 15.1°
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B. 15.7°
C. 74.3°
D. 74.9°
98. In
is a right angle,
and
Which expression represents the length of
?
A.
B.
C.
D.
99. John is walking home with his younger brother, Don. Their home is on the opposite corner of a
rectangular lot with dimensions of 500 feet by 800 feet. John decides to walk along two sides of the lot,
while Don takes the direct diagonal path home.
About how much farther does John walk than Don?
A. 143 feet
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B. 300 feet
C. 357 feet
D. 943 feet
100. A roof support is built according to the diagram shown below.
What is the height of the roof in yards?
A. 18
B.
C.
D. 36
101. Right triangle DEF is shown below.
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What is DF to the nearest tenth of a meter?
A. 10.7
B. 11.6
C. 25.1
D. 29.7
102. Right triangle RST is shown below with the dimensions given in feet (ft).
Which is closest to RT?
A. 6.4
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B. 7.1
C. 12.5
D. 15.7
103. Kristen created a space in her yard for a garden. She had three landscape timbers, each 8 feet in length.
She positioned them in the form of a triangle, as shown in the drawing below. She drove a stake in the
ground at Point C and another stake halfway between Points A and B, at Point D. She then ran a string
between the two stakes to divide the planting area in half so she could plant half the garden with flowers
and the other half with tomatoes.
• What is the measure of
• What is the length of
Show all work or explain your answer.
and the length of
Show all work or explain your answer.
• What is the total area of Kristen’s garden? Show all work or explain your answer.
104. The diagonal of a small square tabletop is 30 inches long. What is the length of each side of the tabletop
in inches?
A. 15
B.
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C.
D.
105. Which of the following equations can be used to verify the identity
A.
B.
C.
D.
106. In
feet, and
feet. What is the approximate area of
feet?
A. 43
B. 541
C. 625
D. 1083
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in square
107. A right triangle with dimensions given in units is shown below.
What is the value of x in units?
A.
B.
C.
D.
108. A manufacturer is designing a square computer chip with a gold filament along its perimeter.
If the diagonal of the chip is
surround the chip?
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millimeters (mm), what is the length of the gold filament that will
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A.
B.
C. 9 mm
D. 24 mm
109. In
Which ratio represents the cosine of Angle Q?
A.
B.
C.
D.
110. Brandon sights a helicopter above a building that is 200 feet away at an angle of elevation of 30º. To the
nearest foot, how high above the ground is the helicopter?
A. 100
B. 115
C. 170
D. 173
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111. The dimensions of
shown below are in units.
Which ratio represents the value of
A.
B.
C.
D.
112. Which of the following equations could be used to find the value of x in the right triangle below?
A.
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B.
C.
D.
113. A 13-foot ladder is resting against a building 12 feet above the ground.
What is the angle formed by the ladder and the ground?
A. 23°
B. 43°
C. 47°
D. 67°
114. From a watch site on a ship, the angle of depression to a raft is 10 degrees. The site is 94 feet above sea
level.
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How far is the raft from the ship?
A. 94 feet
B. 92 feet
C. 123 feet
D. 533 feet
115. In
and the length of the hypotenuse is 10 units. Using the
information below, what is the length of
A. 2.9 units
B. 4.8 units
C. 5.5 units
D. 8.7 units
116. The figure below shows a right triangle and a rectangle.
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What is the area of the figure? Round your answer to the nearest whole number.
A. 72 in.
B. 60 in.
C. 55 in.
D. 42 in.
117. Part of a two-column proof is shown.
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Which conclusion can be derived from this proof?
A. The sine and the cosine of vertical angles are equal.
B. The sine and the cosine of congruent angles are equal.
C. The sine and the cosine of supplementary angles are equal.
D. The sine and the cosine of complementary angles are equal.
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118. The isosceles right triangle below has an area of 98 square feet.
What is the length of the hypotenuse in feet?
A. 14
B. 19.8
C. 24.2
D. 28
119. In the figure below, what is the sin ?
A.
B.
C.
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D.
120.
Tom is feet tall. If Tom stands 30 feet from the base of an apple tree looking up at an apple in the tree
at an angle of sight of 48°, how far is the apple from the ground?
A. 25.6 feet
B. 27.8 feet
C. 33.2 feet
D. 38.8 feet
121. A right triangle is shown below.
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Which expression represents the value of
A.
B.
C.
D.
122. Diagonal
divides rectangle PQRS into two congruent triangles as shown below.
What is the length of
in feet?
A.
B.
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C.
D.
123. Roy drove his boat from a dock due north for 6 miles. He then turned and drove the boat due west for
about 8 miles and dropped anchor. Approximately how many miles from the dock did Roy drop
anchor?
A. 2
B. 5.3
C. 10
D. 14
124. The top of an 18-foot ladder touches the side of a building 14 feet above the ground. Approximately
how far from the base of the building should the bottom of the ladder be placed?
A. 4.0 feet
B. 8.0 feet
C. 11.3 feet
D. 16.0 feet
125. Robert leaves his home to go to his office. He drives 6 km due north and then 4 km due east.
Approximately what is the shortest distance from Robert’s home to his office, in kilometers?
A. 6.2
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B. 7.0
C. 7.2
D. 10.0
126. In the figure below, what is sin
A.
B.
C.
D.
127. In
measures 90 degrees. Which statement must be true?
A.
B.
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C.
D.
128.
In a right triangle, if tan
, then what is sin x?
A.
B.
C.
D.
129. In
and
units. What is the length of the altitude from Vertex M?
A. 25 sin 29°
B. 25 tan 29°
C. 25 sin 61°
D. 25 tan 61°
130.
In a right triangle, if
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, what is
?
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A.
B.
C.
D.
131.
In a right triangle, if sin
then what is tan x?
A.
B.
C.
D.
132. A right triangle has legs of lengths 1 cm and
cm and a hypotenuse of length 2 cm. What must be the
measures of its two non-right angles?
A. 30° and 60°
B. 45° and 45°
C. 40° and 50°
D. 35° and 55°
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133. The figure below shows right triangles inside a rectangle.
Based on the figure, which equation(s) are true?
I.
II.
III.
A. I only
B. I and III only
C. II and III only
D. I, II, and III
134. Gary used landscape timbers to create a border around a garden shaped like a right triangle. The longest
two timbers he used are 12 feet and 15 feet long. Which is closest to the length, in feet, of the shortest
timber?
A. 3
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B. 5.2
C. 7.3
D. 9
135. In a 30°-60°-90° triangle, the length of the hypotenuse is 12 inches. What is the length, in inches, of the
side opposite the 60° angle?
A. 6
B.
C.
D. 24
136. A company makes triangular flags as modeled in the diagram below.
Which measurement is the closest approximation for the length x in inches?
A. 7.5
B. 8.7
C. 10.6
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D. 15
137. The right triangles shown below are similar.
Which equation involving
is correct?
A.
B.
C.
D.
138. A circus elephant is being led up a 12-foot-long ramp to a trailer that is 4 feet above the ground.
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Which equation could be used to find the angle between the ramp and the ground?
A.
B.
C.
D.
139. Which of the following is equal to cos 30°?
A. cos 60°
B. cos 90°
C. sin 30°
D. sin 60°
140. Jen is on the platform of her boat. She sights the top of a lighthouse at an angle of 30º as shown below.
She knows that the height of the lighthouse is 50 meters.
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How far is Jen from the base of the lighthouse, in meters?
A.
B.
C.
D.
141. Right triangle DEF is shown below with the dimensions given in units.
Which measurement is closest to the value of x in units?
A. 4.8
B. 5.1
C. 13.2
D. 14.9
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142. A right triangle is shown in the figure below.
What is the value of x?
A. 5
B. 10
C. 15
D. 20
143. If cos(180°) = –1, what is sin(180°)?
A. –1
B. 0
C. 1
D. 2
144. Cleo is looking at an airplane flying at an altitude of 3 miles. Her angle of elevation is 37 degrees.
About how far is the land distance from Cleo to the plane?
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A. 2 miles
B. 4 miles
C. 5 miles
D. 7 miles
145. A square tile with a side length of
inches is cut diagonally. What is the length of the cut in inches?
A.
B.
C.
D.
146. Jeremy likes to ride his bike to his friend Khaleel’s house. If he takes
the road, he rides 3.6 miles east and then 1.5 miles north. There is also
a path that goes through the woods directly from Jeremy’s house to
Khaleel’s house.
Part A. To the nearest degree, what is the angle shown between the
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road and the path? Use trigonometric functions to calculate the angle.
Part B. To the nearest tenth of a mile, how much farther is it to go
by the road than to go by the path? Show your work.
Part C. One day Jeremy biked from his house to Khaleel’s house on the
path, and then he returned by the road. He timed himself and found
that it took the same amount of time both ways. On the road Jeremy
rode at a speed of 13 miles per hour. To the nearest mile per hour,
how fast was he going on the path through the woods? Explain your
reasoning.
Part D. Another path goes north off the road at a point 2.4 miles from
Jeremy’s house. If Jeremy rode 2.4 miles on the road, turned onto the
path going north, and then connected with the other path to go the rest
of the way to Khaleel’s house, how far would he travel? Show your work
and round your answer to the nearest tenth of a mile.
Use words, numbers, and/or pictures to show your work.
147. Which statement is not true?
A.
B.
C.
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D.
148. Sina played basketball on a rectangular court that was 74 feet by 42 feet. After the game, she walked
across the court diagonally from one corner to the opposite corner. Approximately what distance did
Sina walk in feet?
A. 58
B. 61
C. 85
D. 116
149. If cos(0) = 1, what is sin(0)?
A. –1
B. 0
C. 1
D. 2
150. The measures of the sides of triangle ABC are a, b, and c. The height is
h.
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Part A. Based on the measures shown in the figure, what is the area of
triangle ABC? Using the shaded right triangle, what is the sine of angle
C? Based on the expression found for
what is h? Substitute that
value for h into the formula for the area of the triangle to give a formula
for the area of the triangle.
Part B. Instead of using the base and the height of a triangle to find the
area, what would need to be known to find the area of a triangle using
the formula you derived in Part A?
Use words, numbers, and/or pictures to show your work.
151. A city park has three pavilions located within its boundaries. The locations of the pavilions and the
distances, in meters, between them are shown in the diagram below.
Which measurement is closest to the value of x, the distance between Pavilion #1 and Pavilion #3?
A. 69 meters
B. 87 meters
C. 98 meters
D. 109 meters
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152.
In
shown below, the altitude from Point P to
is designated l.
Which equation can be used to find the area of the triangle, A, in terms
of its side lengths and angle Q?
A.
B.
C.
D.
153. A pipe is to be installed to connect two water towers, located at Points A and B, as shown in the figure
below.
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The distance from Point C to the tower at Point A is 1.2 miles, while the distance from Point C to the
tower at Point B is 1.8 miles. If
what is the distance, to the nearest tenth of a mile,
between the water towers?
A. 1.5
B. 1.8
C. 2.0
D. 2.2
154. A parallelogram has sides 15 centimeters and 11 centimeters long with
angles 130° and 50°. What is the approximate length of the longer
diagonal of the parallelogram?
A. 11.6 centimeters
B. 15.4 centimeters
C. 18.6 centimeters
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D. 23.6 centimeters
155.
Lori wants to derive the area formula,
draws a perpendicular line segment from
for
to the base of
In order to derive the formula, Lori
A diagram of
is shown below.
Which equation could be used to derive the area formula for this triangle?
A.
B.
C.
D.
157. The magnitude of the resultant force, F, produced by two forces with magnitudes of 25 newtons and 40
newtons can be represented by the unknown length of the triangle shown below.
What is the magnitude of F?
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A. 41.3 newtons
B. 47.2 newtons
C. 52.4 newtons
D. 65.0 newtons
158. A triangle and some of its dimensions are shown below.
Which expression can be used to find the measure, in degrees, of
A.
B.
C.
D.
160. Sam is hiking on a trail. He leaves the trail and turns onto Path 1. Path
1 makes a 45° angle with the trail. After walking 300 meters (m) straight on
Path 1, he turns 75° to Path 2, heading back toward the main trail, as shown
in the figure.
Assuming that the trail and the two paths are straight lines, approximately
how far does Sam need to walk on Path 2 to get back to the trail?
A. 212 m
B. 245 m
C. 424 m
D. 580 m
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163. Triangle JKL and some of its measurements are shown below.
Which measurement is closest to the length of
A. 11.0 cm
B. 13.6 cm
C. 14.2 cm
D. 14.8 cm
164.
Marcus wants to prove the Law of Sines:
. He starts by drawing the triangle shown and the
three altitudes. He uses the formula for the area of a triangle to write
Which two substitutions are needed to show
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.
A.
and
B.
and
C.
and
D.
and
166. Quadrilateral KLMN with diagonal
If
and
is shown below.
which is closest to the length of
A. 6.2 cm
B. 6.4 cm
C. 6.9 cm
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?
D. 7.2 cm
167. In Parallelogram PQRS,
centimeters,
centimeters, and
centimeters as shown.
What is the measure of Angle QPS to the nearest tenth of a degree?
A. 48.4°
B. 51.4°
C. 60.7°
D. 70.9°
169. Caleb placed an 8-foot ladder against his house. The base of the ladder was 2 feet away from the vertical
side of the house along a straight downward-sloped surface, as shown in the diagram below.
The measure of the angle between the ladder and the house is 14°. Which is closest to d, the distance from the
base of the house to the point where the top of the ladder touches the house?
A. 6.9 feet
B. 7.3 feet
C. 7.7 feet
D. 8.3 feet
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170. From a point at ground level 120 feet from the base of a building, the angle of elevation of the top of the
building is 68°.
What is the height, to the nearest foot, of the building?
A. 111
B. 297
C. 320
D. 371
171. Bobby wants to calculate the area of
shown below.
Which formula can be used to calculate the area of
A.
B.
C.
D.
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172. Mary wants to calculate the area of
.
What would be the first step in deriving the formula to calculate the area of
A. draw
B. draw
C. draw
D. draw
173. Two people, Julio and Marissa, are both looking at a plane in the sky to
their east. From Julio's point of view, the plane is 87° from the
horizontal ground. From Marissa's point of view, the plane is 88° from
the horizontal ground. Julio and Marissa are 200 yards apart from each
other.
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How high is the plane above the ground, rounded to the nearest yard?
A. 11,437 yards
B. 11,444 yards
C. 11,449 yards
D. 11,453 yards
175. Triangle PQR has angles of 80°, 60°, and 40° as shown in the figure.
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When QR = 14, which value is closest to the length of
A. 7.0
B. 9.1
C. 10.5
D. 12.3
176. In
and
What is the length, to the nearest tenth of a unit, of
A. 7.4 units
B. 9.8 units
C. 14.4 units
D. 15.6 units
178.
Cecelia is trying to find the length of
She sets up the proportion
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in triangle DEF shown below.
Which statement best explains whether or not Cecelia’s method is
correct?
A. Cecelia is correct because she used the measures of the angles
adjacent to
and the correct proportions.
B. Cecelia is not correct because she should have put 12 under
and DF under
C. Cecelia is not correct because she should have used the law of
cosines.
D. Cecelia is not correct because she should have used
above DF.
186. Train A and Train B left a station at the same time, each traveling on
straight paths that intersected to form a 60° angle with each
other. After 30 minutes, Train A had traveled 20 miles and Train B had
traveled 23 miles. What was the approximate distance between the
trains at this time?
A. 11.50 miles
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B. 21.66 miles
C. 26.44 miles
D. 37.27 miles
189. In the triangle shown below, what is the measure of the smallest angle,
rounded to the nearest degree?
A.
B.
C.
D.
190. Tom knows that the formula for the area of a triangle is
For the following triangle, Tom knows the lengths of sides a, b, and c, along
with the measures of angles A, B, and C, but he does NOT know the height
(h).
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Based on the values that Tom does know, how can he determine the height
of the triangle?
A. Find the sine ratio using angle B or angle C.
B. Determine the average value of sides b and c.
C. Find the cosine ratio using angle B or angle C.
D. Determine the sum of all three sides and then divide by 3.
191. Samantha is estimating the width of a lake. She stands at Point B and looks through a long-range scope.
She sees a boat shed at Point A that is about 9 miles away and a tall tree at Point C that is about 7 miles
away.
Which of the following is closest to the distance, in miles, across the lake from Point A to Point C?
A. 9.7
B. 10.6
C. 11.4
D. 12.9
193. The Forest Service builds three rest stops at positions designated D, Y,
and L, enclosing a triangular region. The distance DY is 5 miles, the
distance LY is 8 miles, and
What is the area of the enclosed
region, to the nearest 0.1 square mile?
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A. 10.6
B. 15.6
C. 25.0
D. 34.8
195. The locations of three baseball players are shown in the diagram below.
Which measurement, in yards, is closest to the straight-line distance between Matthew and Troy?
A. 14.1
B. 22.8
C. 25.5
D. 31.2
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197. In the triangle shown below, what is the measure, in degrees, of x,
rounded to the nearest whole number?
A. 57º
B. 65º
C. 77º
D. 87º
198. A light pole is supported by two wires that extend from near the top of
the pole and are anchored to stakes on either side of the pole. The
wires meet at an angle of 72º. One of the wires forms an angle of 68º
with the ground and has a length of 12 meters (m). Approximately how
far apart are the two stakes that anchor the two wires to the ground?
A. 12.31 m
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B. 17.31 m
C. 17.75 m
D. 29.31 m
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