Trigonometry (Law of Sine and Law of Cosine)
Review Quiz (with calculator)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the triangle. 1)
1)
A) C = 75°, c ≈ 4.2, a ≈ 3.8
B) C = 15°, c ≈ 3.8, a ≈ 4.2
C) C = 75°, c ≈ 4.2, a ≈ 2.2
D) C = 15°, c ≈ 1.1, a ≈ 2.2
2) B = 72°, b = 15, c = 8
2)
A) C = 35.7°, A = 72.5°, a ≈ 15.4
B) C = 30.5°, A = 77.5°, a ≈ 15.4
C) Cannot be solved
D) C = 30.5°, A = 77.5°, a ≈ 21.6
State whether the given measurements determine zero, one, or two triangles. 3) C = 30°, a = 32, c = 16 A) Two
3) B) Zero
C) One
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. 4)
4)
22 47° 27 A) No triangle is formed. B) B = 85.2°, C = 47.8°, a ≈ 20.1 C) B = 80.2°, C = 52.8°, a ≈ 20.1 D) The triangle cannot be solved with the Law of Sines.
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Solve. 5) A ranger in fire tower A spots a fire at a direction of 40°. A ranger in fire tower B, which is 28 miles directly east of tower A, spots the same fire at a direction of 116°. How far from tower A is the fire? A) 33 miles
B) 26 miles
C) 24 miles
5)
D) 22 miles
Solve the triangle. 6) a = 6, b = 11, c = 9
6)
A) A ≈ 33°, B ≈ 95.1°, C ≈ 51.9°
B) A ≈ 33°, B ≈ 92.1°, C ≈ 54.9°
C) A ≈ 33°, B ≈ 54.9°, C ≈ 92.1°
D) No triangles possible
Solve the problem. 7) To find the distance between two small towns, an electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible. If the distance from the EDM to the towns is 4.1 miles and 4.5 miles and the angle between the two lines of sight is 37°, what is the distance between the towns? Round your answer to the nearest tenth of a mile. A) 2.8 miles
B) 4.7 miles
C) 7.2 miles
7)
D) 8.2 miles
Solve the triangle. 8)
8)
A) A = 56.8∘, B = 74.4∘, C =48.8∘ C) A = 56.8∘, B = 48.8∘, C =74.4∘
B) A = 48.8∘, B = 56.8∘, C =74.4∘ D) A = 74.4∘, B = 48.8∘, C =56.8∘
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Answer Key Testname: TRIG REVIEW (LAWS)
1) 2) 3) 4) 5) 6) 7) 8)
A B C D B B A C
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