Analytic Geometry A Accelerated Week 3   Page 35 of 51    Analytic Geometry A ‐ Accelerated Week 3  Lesson 2.1    Introduction to Right Triangle Trigonometry   Lesson 2.2    Sine Ratio  Lesson 2.3    Cosine Ratio  Lesson 2.4    Tangent Ratio   Lesson 2.5    Review   Lesson 2.6    Inverse Trigonometric  Ratios  Lesson 2.7    Solve Right Triangles  Lesson 2.8    Solve Right Triangles in Applied Problems    Before working the problems, study the lesson listed above each problem set.  Record the answers on the answer sheet. Turn in the answer sheet to be graded.     For some problem sets, answer boxes are given. Choices may be used more than  once if necessary.    Lesson 2.1    Introduction to Right Triangle Trigonometry   True or False. Choose ‘A’ for True or ‘B’ for False.  1.    The word “trigonometry” comes from the Greek words that mean “triangle measurement.”  2.    The study of trigonometry did not begin until long after the beginning of the Christian era.  3.    The longest side of any right triangle is the hypotenuse.  4.    A right triangle contains one right angle and two acute angles.  5.    The hypotenuse of a right triangle can be opposite an acute angle of a triangle.  6.  The legs of a right triangle form the right angle.          Analytic Geometry A Accelerated Week 3   Page 36 of 51    Multiple Choice.  Use the given triangle to answer problems 7‐11.          A         C                            B                                  7.    Which of the following is the side opposite of  A ?    A)     AB                                    B)     BC                                   C)        AC                                D)    B     8.    Which of the following is the side opposite of  B ?           A)     AC                                    B)     BC                                   C)        AB                                D)    B     9.    Which of the following is the hypotenuse?          A)     AC                                    B)     BC                                   C)        AB                                D)  C     10.   Which of the following is the side adjacent to  A ?          A)     AB                                    B)     AC                                   C)        BC                                D)    B     11.   Which of the following is the side adjacent to  B ?          A)     AB                                    B)     AC                                   C)        BC                                D)    A     Lesson 2.2 Sine Ratio         A         C                            B                                  12.    What is the sine ratio for  A ?             A)     BC AC                                    B)     BC AB                                   C)        AC AB                                D)    AB BC   13.    What is the sine ratio for  B ?             A)     BC AC                                    B)     .

1. Analytic Geometry A Accelerated Week 3 Page 35 of 51
Analytic Geometry A ‐ Accelerated Week 3
Lesson 2.1 Introduction to Right Triangle Trigonometry
Lesson 2.2 Sine Ratio
Lesson 2.3 Cosine Ratio
Lesson 2.4 Tangent Ratio
Lesson 2.5 Review
Lesson 2.6 Inverse Trigonometric Ratios
Lesson 2.7 Solve Right Triangles
Lesson 2.8 Solve Right Triangles in Applied Problems
Before working the problems, study the lesson listed above each
problem set.
Record the answers on the answer sheet. Turn in the answer she
et to be graded.
For some problem sets, answer boxes are given. Choices may be
used more than
once if necessary.

2. Lesson 2.1 Introduction to Right Triangle Trigonometry
True or False. Choose ‘A’ for True or ‘B’ for False.
1. The word “trigonometry” comes from the Greek words that
mean “triangle measurement.”
2. The study of trigonometry did not begin until long after the
beginning of the Christian era.
3. The longest side of any right triangle is the hypotenuse.
4. A right triangle contains one right angle and two acute angl
es.
5. The hypotenuse of a right triangle can be opposite an acute
angle of a triangle.
6. The legs of a right triangle form the right angle.
Analytic Geometry A Accelerated Week 3 Page 36 of 51
Multiple Choice.
Use the given triangle to answer problems 7‐11.
A
C B

3. 7. Which of the following is the side opposite of
A) AB B) BC
C) AC D)
8. Which of the following is the side opposite of
A) AC B) BC
C) AB D)
9. Which of the following is the hypotenuse?
A) AC B) BC
C) AB D)
10. Which of the following is the side adjacent to
A) AB B) AC
C) BC D)
11. Which of the following is the side adjacent to
A) AB B) AC
C) BC D)
Lesson 2.2 Sine Ratio

4. A
C B
12. What is the sine ratio for
A)
BC
AC
B)
BC
AB
C)
AC
AB
D)
AB
BC
13. What is the sine ratio for
A)
BC
AC
B)

5. BC
AB
C)
AC
AB
D)
AB
BC
Analytic Geometry A Accelerated Week 3 Page 37 of 51
Find the indicated trigonometric ratio. Write each answer as a fr
action in simplest form.
14. sin R 16. sin R
15. sin S 17. sin S
18. sin R 20. sin R

6. 19. sin S 21. sin S
Choices for 14‐21
A)
24
26
B)
44
125
C)
20
21
D)
12
13
E)
28
53
AB)
10
24
AC)

7. 20
29
AD)
125
117
AE)
45
53
BC)
21
20
BD)
5
13
BE)
44
117
CD)
21
29

8. CE)
28
45
DE)
117
125
ABC)
90
106
Analytic Geometry A Accelerated Week 3 Page 38 of 51
Find the indicated trigonometric value. Round to 4 decimal plac
es, if necessary.
22. sin A 24. sin A
23. sin B 25. sin B

9. Choices for 22‐25
Use sine to find the value of x to the nearest tenth.
26. 27. 28.
Choices for 26‐28
A) 20.1 B) 21.4 C) 23.5 D) 25.2 E) 28.1
AB) 30.8 AC) 32.6 AD) 33.3 AE) 34.1 BC)
35.6
BD) 36.9 BE) 38.0
A) 0.3243 B) 0.3429 C) 0.90 D) 0.7423 E) 1 AB)
3.5714
AC) 0.9459 AD) 0.2917 AE) 0.9059 BC) 0.28
BD) 1.3472
BE) 0.96
CD) 0.4235 CE) 0.47 DE) 0.6701 ABC) 1.1039

10. Analytic Geometry A Accelerated Week 3 Page 39 of 51
Lesson 2.3 Cosine Ratio
A
C B
29. What is the cosine ratio for
A)
BC
AC
B)
BC
AB
C)
AC
AB
D)
AB
BC
30. What is the cosine ratio for

11. A)
BC
AC
B)
BC
AB
C)
AC
AB
D)
AB
BC
Find the indicated trigonometric ratio. Write each answer as a fr
action in simplest form.
31. cos R 33. cos R
32. cos S 34. cos S
Choices for 31‐34
A)

12. 24
26
B)
44
125
C)
20
21
D)
12
13
E)
28
53
AB)
10
24
AC)
20
29
AD)

13. 125
117
AE)
45
53
BC)
21
20
BD)
5
13
BE)
44
117
CD)
21
29
CE)
28
45
DE)

14. 117
125
ABC)
90
106
Analytic Geometry A Accelerated Week 3 Page 40 of 51
35. cos R 37. cos R
36. cos S 38. cos S
Choices for 35‐38
A)
24
26
B)
44

15. 125
C)
20
21
D)
12
13
E)
28
53
AB)
10
24
AC)
20
29
AD)
125
117
AE)
45

16. 53
BC)
21
20
BD)
5
13
BE)
44
117
CD)
21
29
CE)
28
45
DE)
117
125
ABC)
90

17. 106
Find the indicated trigonometric value. Round to 4 decimal plac
es, if necessary.
39. cos A 41. cos A
40. cos B 42. cos B
Choices for 39‐42
A) 0.3243 B) 0.3429 C) 0.90 D) 0.7423 E) 1 AB)
3.5714
AC) 0.9459 AD) 0.2917 AE) 0.9059 BC) 0.28
BD) 1.3472
BE) 0.96
CD) 0.4235 CE) 0.47 DE) 0.6701 ABC) 1.1039

18. Analytic Geometry A Accelerated Week 3 Page 41 of 51
Use cosine to find the value of x to the nearest tenth.
43. 44. 45.
Choices for 43‐45
Lesson 2.4 Tangent Ratio
A
C B
46. What is the tangent ratio for
A)
BC
AC
B)
AC
BC
C)

19. BC
AB
D)
AC
AB
47. What is the tangent ratio for
A)
BC
AC
B)
AC
BC
C)
BC
AB
D)
AC
AB
A) 4.3 B) 5.6 C) 8.2 D) 9.3 E) 13.1 AB) 14.0

20. AC) 15.0 AD) 26.4 AE) 29.6 BC) 34.8 BD) 36.9
BE) 38.7
CD) 50.5 CE) 51.3 DE) 65.9 ABC) 68.9 ABD) 75.8
ABE) 78.3
Analytic Geometry A Accelerated Week 3 Page 42 of 51
Use the figure below to answer the following.
48. Find tan as a fraction in simplest form.
49. Find tan as a decimal rounded to four decimal places.
50. Find tan as a fraction in simplest form.
51. Find tan as a decimal rounded to four decimal places.
Use the figure below to answer the following.
52. Find tan as a fraction in simplest form.
53. Find tan as a decimal rounded to four decimal places.
54. Find tan as a fraction in simplest form.

21. 55. Find tan as a decimal rounded to four decimal places.
Choices for 48‐55
A)
B) 0.9524 C) 0.5892 D)
E) 1.0500 AB) 0.5077
AC)
21
20
AD) 0.8615 AE) BC) BD) 1.6970 BE)
CD) CE) 0.5893 DE) .6897
ABC) ABD) 0.7241 ABE) 0.9523
Analytic Geometry A Accelerated Week 3 Page 43 of 51
Find the value of x to the nearest tenth.
56. 57. 58.
Choices for 56‐58

22. A) 15.5 B) 42.2 C) 18.4 D) 10.9 E)
37.2
AB) 14.4 AC) 3.4 AD) 13.9 AE) 25.5 BC) 143.8
Lessons 2.2, 2.3 and 2.4 Sine Ratio, Cosine Ratio, and Tangent
Ratio
Use a sine, cosine, or tangent ratio to find the value of x
. Round decimals to the nearest tenth.
Answer choices are on the following page.
59. 60. 61.
Choices for 59‐61
A) 6.8 B) 7.6 C) 12.0 D) 12.4 E) 20.2 AB)
22.4
AC) 22.6 AD) 26.0 AE) 35.7 BC) 36.3 BD)
40.6 BE) 42.5
CD) 56.3 CE) 56.4 DE) 76.1 ABC) 77.3 ABD)
98.8 ABE) 103.1
Analytic Geometry A Accelerated Week 3 Page 44 of 51

23. 62. 63. 64.
Choices for 62‐64
A) 6.8 B) 7.6 C) 12.0 D) 12.4 E) 20.2 AB)
22.4
AC) 22.6 AD) 26.0 AE) 35.7 BC) 36.3 BD)
40.6 BE) 42.5
CD) 56.3 CE) 56.4 DE) 76.1 ABC) 77.3 ABD)
98.8 ABE) 103.1
True or False. Choose ‘A’ for true or ‘B’ for false.
65. Tangent ratios of complementary angles are reciprocals.
66. The sine ratio can be greater than 1.
67. The cosine ratio is never greater than 1.
68. The tangent ratio involves the legs of a right triangle.
69. As acute angles get larger, the sine ratio gets larger.
70. The tangent ratio can be greater than 1.
71. The sine of an angle and the cosine of its complement are e
qual.

24. 72. As acute angles get larger, the cosine ratio gets larger.
73. Trigonometric ratios can be found by using a table of trigo
nometric values or a calculator.
74.
75.
Analytic Geometry A Accelerated Week 3 Page 45 of 51
Find the indicated trigonometric value for triangle XYZ. Round
the answer to four decimal places.
76. sin 77. 78.
79. 80.
Choices for 76‐80
A) 0.2917 B) 0.9600 C) 1.0417 D) 0.8000 E)
0.7500 AB) 0.2800
AC) 1.6667 AD) 3.5714 AE) 0.6000 BC) 1.3333
BD) 3.4286 BE) 1.2500
Lesson 2.5 Review

25. Find the missing side in a right triangle. Leave radicals in simpl
ified form.
81. If the legs are 8 and 15, find the hypotenuse.
82. If one leg is 40 and the hypotenuse if 41, find the other le
g.
83. If the legs are 5 and 10, find the hypotnenuse.
Find the missing angle.
84. Find the complement of
85. Find the third angle of a triangle if two angles are
86. Find the other acute angle of a right triangle if one acute a
ngle is
Choices for 81‐86
A) 4 B) 9 C) 12 D) 17 E) 23 AB) 30
AC) 81 AD) 3 AE) 5
BC) 5 3 BD) 5 5 BE) CD) CE)
DE) 4 ABC) ABD)
Analytic Geometry A Accelerated Week 3 Page 46 of 51

26. Draw a right triangle ABC with the right angle at C for each pro
blem. Find the indicated angle or
side. Leave radicals in simplified form.
87. Find c if and
88. Find a if and
89. Find b if and
90. Find if
91.
Choices for 87‐91
A) 4 B) 9 C) 12 D) 17 E) 23 AB) 30
AC) 81 AD) 3 AE) 5
BC) 5 3 BD) 5 5 BE) CD) CE)
DE) ABC) ABD)
Lesson 2.6 Inverse Trigonometric Ratios
Let
be an acute angle in a right triangle. Approximate the measure
of to the nearest tenth
of a degree.
92.

27. 93.
94.
95.
96.
97.
98.
99. cos 0
100.
101.
Choices for 92‐101
A) B) C) D) E)
AB)
AC) AD) AE) BC)
BD) BE) 7
CD) CE) DE) ABC)
ABD)
Analytic Geometry A Accelerated Week 3 Page 47 of 51

28. Find to the nearest degree.
102. 103. 104.
Draw a right triangle ABC with right angle at C for each proble
m. Find the indicated angle to the
nearest degree.
105. Find if and
106. Find if and
107. Find if and
108. Find if AC and
109. Find if and
Choices for 102‐109

29. A) B) C) D) E) AB)
AC) AD) AE) BC) BD)
Analytic Geometry A Accelerated Week 3 Page 48 of 51
Lesson 2.7 Solve Right Triangles
Use the figures below to answer problems 110‐123.
Use a tangent, sine, or cosine ratio to find the value of the indic
ated variable. Round decimals to
the nearest tenth.
110. t
111. u
112. x
113. y
114. g
115. h

30. 116. a
117. b
118. c
119. d
120. m
121. n
122.
123.
Choices for problems 110‐123
A) 3.9 B) 5.8 C) 7.0 D) 7.8 E) 8.2 AB) 8.8
AC) 8.9
AD) 12.0 AE) 20.1 BC) 24.9 BD) 35.6 BE) 56.6
CD) CE)
Analytic Geometry A Accelerated Week 3 Page 49 of 51
Lesson 2.8 Solve Right Triangles in Applied Problems
124. Let x
represent the width of a river. Use the drawing to determine the
width of the
river. Round decimals to the nearest hundredth if necessary.

31. A) 25.36 .ft
B) 27.98 .ft
C) 54.38 .ft
D) 128.67 .ft
125. Let x
represent the height of a tower. Use the drawing to determine t
he height of the
tower. Round decimals to the nearest hundredth if necessary.
A) 57.85 .ft
B) 68.94 .ft
C) 107.26 .ft
D) 140.02 .ft
126. Find the distance d
from a house on the shore to a house on the island. An instrume
nt
called a transit is used to find that the measure of
Round decimals to the
nearest hundredth if necessary.
A) 29.73m
B) 44.42m
C) 53.83m

32. D) 59.78m
Analytic Geometry A Accelerated Week 3 Page 50 of 51
127. Ladder You lean a 20 foot ladder against a house. The ba
se of the ladder is 4 feet from
the wall. What angle
does the ladder make with the ground? Round decimals to the n
earest
tenth if necessary.
A)
B)
C)
D)
128. Skyscraper You are standing 350 feet away from a skyscr
aper that is 750 feet tall. What
is the angle of elevation from you to the top of the building? Ro
und decimals to the

33. nearest tenth if necessary.
A)
B)
C)
D)
129. Concert You attend a music concert with some friends a
nd sit halfway up the bleachers
in the arena. The angle of depression from the horizontal line to
the stage is your
seat is 45 feet above the stage level, what is your actual distanc
e d from the stage?
Round to the nearest foot.
A) 49 .ft
B) 111 .ft
C) 62 .ft
D) 101 .ft
Analytic Geometry A Accelerated Week 3 Page 51 of 51
The Uniform Federal Accessibility Standards specify that the ra

34. mp angle used for a
wheelchair ramp must be less than or equal to
130. The length of one ramp is 16 feet. The vertical rise is 14 i
nches. Estimate the ramp’s
horizontal distance. Use the Pythagorean Theorem. (Hint: Cha
nge 16 feet into inches.)
131. Estimate the ramp’s angle.
132. Does this ramp meet the Uniform Federal Accessibility St
andards?
Choices for 130‐132
A) B) C) D) 7.75 .ft
E) 191.49 .in AB) 192.51 .in AC) yes AD) no
133. A forest ranger spotted an unattended campfire from his p
osition in a 75 foot tall tower.
The angle of depression as he looks toward the campfire is
What is the distance from
the base of the tower to the campfire?
A) 73.9 .ft B) 298.6 .ft

35. C) 425.3 .ft D) 523.5 .ft
134. You lean a 24 foot ladder against a house. The base of the
ladder is 4.5 feet from the
house. Find the angle of elevation.
A) B)
C) D)
135. A person is flying a kite. What is the angle of elevation th
e string makes with the ground
if the kite is flying 124 feet above the ground and 150 feet of s
tring is let out?
A) B)
C) D)