Name _______________________________________ Date __________________ Class __________________
MODULE
13
Trigonometry with Right Triangles
Module Exam Review
Write in simplest radical form.
1.
1008 ___________________
2.
72
8. Given that cos 42  0.743, what is the
sine of the complementary angle?
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____________________
Use the figure for 9–10.
Use the figure for 3–5.
9. What is LK rounded to the nearest
hundredth? Show your work.
State each of the following:
3. What is tan D ?
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4. What is sin D ?
10. What is JK rounded to the nearest
hundredth? Show your work.
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5. What is cos D ?
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Use the figure for 11–12.
A right triangle is shown.
11. What is m M ?
6. What is GI? Show your work. Give
answer in simplest radical form.
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________________________________________
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12. What is mO? Explain how you got your
answer.
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7. Are sin and cos reciprocals of each
other? Explain.
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63
Name _______________________________________ Date __________________ Class _________________
MODULE
13
Trigonometry with Right Triangles
Module Exam Review
PQR is shown.
17. What is the area of
nearest tenth?
13. What are the missing side lengths in
PQR ? Explain.
VWX to the
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18. Solve the triangle by finding the lengths
of all the sides and the measures of all
the angles. Show your reasoning.
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TSU is shown.
________________________________________
14. What are the missing side lengths in
TSU? Explain. Keep your answer in
simplified radical form.
________________________________________
________________________________________
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19. Find the side lengths to the nearest
hundredth and the angle measures to
the nearest degree.
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15. What is a Pythagorean Triple?
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16. State whether the following are
Pythagorean Triples or multiples of
Pythagorean Triples.
A 6, 8, 10
Yes
No
B 14, 48, 50
Yes
No
C 25, 25, 100
Yes
No
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64
Name _______________________________________ Date __________________ Class _________________
2. By the converse of the Triangle
GF GI
Proportionality Theorem, if
, then

FH IJ
5? 4
.
FI HJ . Using the lengths given, 
3 2.4
Using cross products, 5(2.4)  4(3) or 12  12.
14.
 4 3
Module Quiz 12 Modified
EC ED
EC ED
B


CA DB
EA EB
EB EA
DB CA
C
D


ED EC
EB EA
2. C
3. A
4. B
5. B
6. B
1. A
2
2
3. Point P is
 of the distance from
23 5
A to B. Run  8  2  10; rise  6  1
2
2
2
5;
of run  ( 10)  4 ;
of rise 
5
5
5
2
(5)  2 ; x-coordinate of point P  2  4 
5
2; y-coordinate of point P  1  2  3.
The coordinates of point P are (2, 3).
4. A indirect measure
building’s height building’s shadow
B

person’s height
person’s shadow
7. MN  2(429)  858 ft
GF DG
8.

DG GE
9. A
10. A
C The building and its shadow along with
the person and his or her shadow form
similar triangles. Therefore, the sides
x 18.5
are in proportion. So, 
;
6 3.2
x
18.5
111
and the height
6
6
;x
6
3.2
3.2
of the building is about 208 feet.
11. B
6 x
12. 
x 42
13. C
14. 12
5. The measure of KL is equal to twice the
measure of MN because KL is the
midsegment of the triangle.
6. MN  2(429)  858 ft
2 x
7. 
; x2  64; x  8
x 32
3 x
8. 
; x2  225; x  15
x 75
6 x
9. 
; x2  252; x  6 7  15.9
x 42
GF DG
10.

DG GE
1.5 DG DG 2
11.
;
 7.5; DG  2.7

DG
5
12. HLJ
LKJ
LKH
13.
4 y
12 z 2
; z  192  8 3 ; 
; 48  y2

y 12
z 16
MODULE 13 Trigonometry with
Right Triangles
Module Quiz 13: B
1. BC
2. AB
7
3.
4
7
4.
8.1
4
5.
8.1
GI
; 2 tan 68  GI; GI  4.95
2
7. No; Sin of an angle is equal to the
opposite side divided by the hypotenuse.
Cosine of an angle is equal to the
adjacent side divided by the hypotenuse.
Both are divided by the hypotenuse so
they are not reciprocals of each other.
6. tan 68 
4
8
; 16  4x  84; 4x  48; x  12

8 4x
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65
Name _______________________________________ Date __________________ Class _________________
8. 0.743
12. 16 3
LK
9. sin 20 
; 8.5(sin 20)  LK; LK  2.91
8.5
2.91
10. tan 20 
; JK(tan 20)  2.91; JK  8
JK
5
11. m M  sin1   ; mM  27
 11
12. The sum of the interior angles of a triangle
are 180, so mO  180  90  27  63.
13. In a 45-45-90 triangle, the hypotenuse is
2 times each leg. So, 12  QR 2 and
QR  8.49.


14. TU  2 8 3  16 3; SU 

3 8 3
13. B
14. 59
15. A
16. A
17. 4 5
18. 63
MODULE 14 Angles in Circles
Module Quiz 14 B

1. 4
 8(3)  24
15. A Pythagorean triple is a set of 3 positive
integers such that a2  b2  c2.
16. A Yes B Yes C No
1
17. A   4.1 7.2 sin 47  10.79 m2 .
2
5
18. To find mF, sin x 
so, mF  59.
5.83
Then mE  90  59  31. To find DF,
52  (DF)2  (5.83)2 or DF is about 2.998 ft.
19. AB  BC, so mB  90
AB  4, BC  8,
2. 45
3. A tangent line intersects the circle at
exactly one point while a secant line
intersects the circle at exactly two points.
4. 7
5. 25
6. 100
7. 90
8. 120
9. Since the angles at points B and D are
right angles, CA is a diameter by the
angle inscribed in a semicircle theorem.
AC  (4  ( 4))2  (4  8)2  80  8.9,
10. 4
 BC 
8
mA  tan 
 tan1    63

 AB 
 4
A and C are complementary, so
mC  90  63  27.
1
11. 30
12. 112
13. 25
14. 60
Module Quiz 13 Modified
15. 60
1. B
2. A
16. Yes; mAOC  180 and AC passes
through the center of the circle.
3. A
17. 9
4. C
Module Quiz 14 Modified
5. B
6. B
1. 20
7. C
2. A
8. 2.91 m
3. B
9. 70
4. A
10. A
5. 120
11. 24
6. B
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66