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
