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Question : Assume triangle ABC has standard labeling : 2152287

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Assume triangle ABC has standard labeling. Determine if AAS, ASA, SSA, SAS, or SSS is given, and decide if the law of sines or the law of cosines should be used to solve the triangle.

1) a, b, and α

A) SSS; law of cosines

B) SSA; law of sines

C) SAS; law of cosines

D) AAS; law of cosines

2) α, b, and c

A) SSS; law of cosines

B) SAS; law of cosines

C) ASA; law of sines

D) SSA; law of sines

3) a, β, and c

A) SAS; law of cosines

B) SSA; law of sines

C) AAS; law of sines

D) ASA; law of cosines

4) a, b, and c

A) SSA; law of cosines

B) SSS; law of cosines

C) ASA; law of sines

D) SSS; law of sines

5) γ, c, and α

A) ASA; law of sines

B) ASA; law of cosines

C) AAS; law of sines

D) AAS; law of cosines

6) γ, b, and c

A) ASA; law of sines

B) SSA; law of sines

C) AAS; law of sines

D) SSA; law of cosines

7) b, c, and β

A) SSS; law of cosines

B) AAS; law of sines

C) SSA; law of cosines

D) SSA; law of sines

8) γ, β, and c

A) AAS; law of sines

B) SSA; law of cosines

C) SSA; law of sines

D) SAS; law of cosines

9) α, γ, and b

A) SSA; law of sines

B) AAS; law of sines

C) ASA; law of sines

D) SAS; law of cosines

10) a, β, and γ

A) AAS; law of cosines

B) AAS; law of sines

C) ASA; law of sines

D) ASA; law of cosines

Solve the triangle. Approximate values to the nearest tenth when appropriate.

11)

A) c = 17, α = 21.9°, β = 48°

B) c = 19.9, α = 17.9°, β = 52°

C) c = 14.1, α = 19.9°, β = 50°

D) No solution

12)

A) α = 29.5°, β = 56.1°, γ = 94.4°

B) α = 27.5°, β = 58.1°, γ = 94.4°

C) α = 25.5°, β = 58.1°, γ = 96.4°

D) No solution

13) γ = 115.4°, a = 4.50, b = 8.07

A) c = 13.7, α = 24.1°, β = 40.5°

B) c = 16.6, α = 20.1°, β = 44.5°

C) c = 10.8, α = 22.1°, β = 42.5°

D) No solution

14) β = 63.5°, a = 12.2, c = 7.8

A) b = 13.2, α = 73.1°, γ = 37.4°

B) b = 11.2, α = 77.1°, γ = 39.4°

C) b = 12.2, α = 75.1°, γ = 41.4°

D) No solution

15) γ = 120.75°, b = 4.7, a = 12.2

A) c = 16.7, α = 45.6°, β = 13.6°

B) c = 15.2, α = 43.8°, β = 15.5°

C) c = 17.4, α = 41.6°, β = 17.6°

D) No solution

16) a = 24, b = 31, c = 42

A) α = 46.8°, β = 34.4°, γ = 98.8°

B) α = 34.4°, β = 23.4°, γ = 122.2°

C) α = 34.4°, β = 46.8°, γ = 98.8°

D) No solution

17) a = 167, b = 186, c = 320

A) α = 26.4°, β = 23.6°, γ = 130°

B) α = 23.6°, β = 26.4°, γ = 130°

C) α = 23.6°, β = 13.2°, γ = 143.2°

D) No solution

18) a = 6.3, b = 13.8, c = 16.9

A) α = 22.7°, β = 48.7°, γ = 108.6°

B) α = 18.7°, β = 50.7°, γ = 110.6°

C) α = 20.7°, β = 50.7°, γ = 108.6°

D) No solution

19) β = 63°30', a = 12.2, c = 7.8

A) b = 12.2, α = 75°7', γ = 41°23'

B) b = 13.2, α = 73°7', γ = 37°23'

C) b = 11.2, α = 77°7', γ = 39°23'

D) No solution

20) γ = 120°45', b = 4.7, a = 12.2

A) c = 17.4, α = 41°37', β = 17°38'

B) c = 16.7, α = 45°37', β = 13°38'

C) c = 15.2, α = 43°51', β = 15°24'

D) No solution

Decide if a triangle exists that satisfies the given conditions.

21) a = 15, b = 12, c = 10

A) Yes

B) No

22) α = 49°, γ = 26°, b = 6

A) No

B) Yes

23) b = 43, c = 25, α = 30°

A) No

B) Yes

24) β = 53°, γ = 29°, b = 11

A) Yes

B) No

25) a = 49, b = 15, β = 50°

A) Yes

B) No

26) b = 50, c = 13, γ = 63°

A) No

B) Yes

27) a = 8, α = 121°, c = 29

A) No

B) Yes

28) a = 10, b = 12, α = 30°

A) No

B) Yes

29) a = 8, b = 16, c = 33

A) Yes

B) No

30) a = 31, α = 134°, c = 24

A) Yes

B) No