Download Trig Test #2 Review: Non

Name: ______________________
Class: _________________
Date: _________
ID: A
Directions for all problems on this test: Round your decimals to three decimal places. You must show
your work. Attach all work to the back of the test when you turn it in.
Trig Test #2 Review: Non-right triangle trig
1. Given triangle ABC with a = 3, A = 40°, and B = 27°, find c.
2. Solve triangle ABC given that A = 47°, B = 52°, and b = 78.
3. Given triangle ABC with a = 10, b = 13, and A = 19°, find c.
4. Find the area of ΔABC. The figure is not drawn to scale.
5. Find the area of ΔABC. The figure is not drawn to scale.
6. Make up an example for which the law of sines will not work and explain why it will not work. Include a
drawing to illustrate your example.
7. Solve ΔABC with A = 33°, a = 6.5, and b = 3.
8. Solve ΔABC with A = 110°, a = 5, and b = 7.3.
9. Given triangle ABC with b = 8, c = 5, and A = 58°, find a.
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Name: ______________________
ID: A
10. Solve triangle ABC given that a = 19, b = 10, and c = 14.
A 50-foot ramp makes an angle of 4.9° with the horizontal. To meet new accessibility
guidelines, a new ramp must be built so it makes an angle of 2.7° with the horizontal.
11. What will be the length of the new ramp?
The roof of a house is being reconstructed to accommodate heavy snows. The current 32-foot
roofline makes an 18.2° angle with the horizontal. The owner has decided to construct the
new roof so that it makes a 50° angle with the horizontal.
12. What will be the length of the new roofline?
13. How much higher will the new roof be?
14. Find the area of ΔABC .
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Name: ______________________
ID: A
15. Use Trigonometry to investigate the lengths of the diagonals of the isosceles trapezoid with bases 4
centimeters and 7 centimeters long and a height of 6 centimeters.
Find XY
Find AX
Find AB
Find cos A
Find BD.
16. Explain when it is appropriate to use the law of sines and when it is appropriate to use the law of cosines
to solve a triangle.
Solve ΔABC.
17.
Find the area of ΔABC.
18.
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Name: ______________________
ID: A
19.
20. Ships Two ships leave Boston Harbor at the same time. What is the distance between ships A and C
after they have traveled 80 kilometers and 70 kilometers respectively?
21. Ravine Width Use the diagram to find the distance across the ravine.
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ID: A
Trig Test #2 Review: Non-right triangle trig
Answer Section
1. ANS:
4.30
PTS: 1
DIF: Level B
REF: MAL21754
TOP: Lesson 13.5 Apply the Law of Sines
KEY: triangle | trigonometry | Law of Sines
BLM: Comprehension
NOT: 978-0-618-65615-8
2. ANS:
C = 81°, a = 72.39, c = 97.76
PTS: 1
DIF: Level B
REF: MAL21756
TOP: Lesson 13.5 Apply the Law of Sines
KEY: solve | triangle | Law of Sines
BLM: Comprehension
NOT: 978-0-618-65615-8
3. ANS:
c = 21.35 or 3.23
PTS: 1
DIF: Level B
REF: MAL21764
TOP: Lesson 13.5 Apply the Law of Sines
KEY: triangle | trigonometry | Law of Sines
BLM: Comprehension
NOT: 978-0-618-65615-8
4. ANS:
2
31.41 cm
PTS: 1
DIF: Level B
REF: MAL21767
TOP: Lesson 13.5 Apply the Law of Sines
KEY: acute | triangle | trigonometry | sine | SAS | area
BLM: Comprehension
NOT: 978-0-618-65615-8
5. ANS:
2
14.67 cm
PTS: 1
DIF: Level B
REF: MAL21768
TOP: Lesson 13.5 Apply the Law of Sines
KEY: area | acute | triangle | trigonometry | sine | SAS
BLM: Comprehension
NOT: 978-0-618-65615-8
6. ANS:
Sample answer: Let m∠A = 40°, b = 20 inches, and a = 5 inches. Using the law of sines,
5
20
20 sin 40°
=
and thus sin B =
, or sin B = 4 sin 40°. But sin B ≠ 4 sin 40° since 4 sin 40°>1.
sin 40° sin B
5
(When trying to construct the triangle, side BC is too short to form a triangle.)
PTS: 1
DIF: Level C
REF: MAL21774 NAT: NCTM 9-12.GEO.1.c
TOP: Lesson 13.5 Apply the Law of Sines
KEY: Law of Sines
BLM: Comprehension
NOT: 978-0-618-65615-8
1
ID: A
7. ANS:
In ΔABC B ≈ 14.6°, C ≈ 132.4°, and c ≈ 8.8.
PTS: 1
DIF: Level B
REF: A2.13.05.FR.10
TOP: Lesson 13.5 Apply the Law of Sines
KEY: Free response | law of sines | acute angle | SSA
BLM: Comprehension
NOT: 978-0-618-65615-8
8. ANS:
No solution. It is not possible to draw the indicated triangle.
PTS: 1
DIF: Level B
REF: A2.13.05.FR.11
TOP: Lesson 13.5 Apply the Law of Sines
KEY: Free response | law of sines | SSA
BLM: Comprehension
NOT: 978-0-618-65615-8
9. ANS:
6.83
PTS: 1
DIF: Level B
REF: MAL21775
TOP: Lesson 13.6 Apply the Law of Cosines
KEY: triangle | Law of Cosines | side
BLM: Comprehension
NOT: 978-0-618-65615-8
10. ANS:
A = 103.4°, B = 30.8°, C = 45.8°
PTS: 1
DIF: Level B
REF: MAL21779
TOP: Lesson 13.6 Apply the Law of Cosines
KEY: triangle | Law of Sines | Law of Cosines
BLM: Comprehension
NOT: 978-0-618-65615-8
11. ANS:
≈90.66 ft
PTS: 1
DIF: Level B
REF: MAL21782
TOP: Lesson 13.6 Apply the Law of Cosines
KEY: Law of Sines
BLM: Application NOT: 978-0-618-65615-8
12. ANS:
≈47.29 ft
PTS: 1
DIF: Level B
REF: MAL21783
TOP: Lesson 13.6 Apply the Law of Cosines
KEY: Law of Cosines
BLM: Application NOT: 978-0-618-65615-8
13. ANS:
≈26.23 ft
PTS: 1
DIF: Level B
REF: MAL21784
TOP: Lesson 13.6 Apply the Law of Cosines
KEY: Law of Cosines
BLM: Application NOT: 978-0-618-65615-8
2
ID: A
14. ANS:
276.96
PTS: 1
DIF: Level B
REF: MAL21785
TOP: Lesson 13.6 Apply the Law of Cosines
KEY: area | heron | triangle
BLM: Comprehension
NOT: 978-0-618-65615-8
15. ANS:
XY = 4 cm; AX = 1.5 cm; AB = 38.25 cm (or 6.18 cm); cos A = 0.24;
2
2
2
BD = AB + AD − 2 ⋅ AB ⋅ AD ⋅ cos A
= 38.25 + 49 – 2( 38.25 )(7)(0.24)
= 66.49 cm
so BD = 66.49 cm ≈ 8.15 cm
PTS: 1
DIF: Level C
REF: MAL21788
TOP: Lesson 13.6 Apply the Law of Cosines
KEY: Law of Cosines | trapezoid | diagonal
BLM: Application
NOT: 978-0-618-65615-8
16. ANS:
Sample answer: Use the law of sines when given the measures of two angles and the length of one side of
a triangle. Use the law of cosines when given the lengths of two sides and the measure of their included
angle, or when given the measures of all three sides.
PTS: 1
DIF: Level C
REF: MAL21789 NAT: NCTM 9-12.COM.2
STA: GA.GPS.MTH.04.6-12.M6P1.d | GA.GPS.MTH.04.6-12.M6P3.a | GA.GPS.MTH.04.6-12.M6P3.b
TOP: Lesson 13.6 Apply the Law of Cosines
BLM: Comprehension
NOT: 978-0-618-65615-8
17. ANS:
C = 145°, a ≈ 4.5, b ≈ 5.9
PTS: 1
DIF: Level B
TOP: Ch. 13 Test, Level A
BLM: Comprehension
18. ANS:
34.6
REF: A2.13.TestA.Eng.19
KEY: Pre-made Test | Law of Sines
NOT: 978-0-618-65615-8
PTS: 1
DIF: Level B
TOP: Ch. 13 Test, Level A
BLM: Comprehension
19. ANS:
158.7
REF: A2.13.TestA.Eng.22
KEY: Pre-made Test | area
NOT: 978-0-618-65615-8
PTS: 1
DIF: Level B
TOP: Ch. 13 Test, Level A
BLM: Comprehension
REF: A2.13.TestA.Eng.23
KEY: Pre-made Test | area
NOT: 978-0-618-65615-8
3
ID: A
20. ANS:
101.6
PTS: 1
DIF: Level B
REF: A2.13.TestB.Eng.25
TOP: Ch. 13 Test, Level B
KEY: Pre-made Test | indirect measurement
BLM: Application NOT: 978-0-618-65615-8
21. ANS:
37 m
PTS: 1
DIF: Level C
REF: A2.13.TestC.Eng.25
TOP: Ch. 13 Test, Level C
KEY: Pre-made Test | indirect measurement
BLM: Application NOT: 978-0-618-65615-8
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