Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
-$\mathrm { B } = 41 ^ { \circ } , \mathrm { a } = 4 , \mathrm {~b} = 3$
A) $\mathrm { A } _ { 1 } = 61 ^ { \circ } , \mathrm { C } _ { 1 } = 78 ^ { \circ } , \mathrm { C } _ { 1 } = 4.5$;
$\mathrm { A } _ { 2 } = 119 ^ { \circ } , \mathrm { C } _ { 2 } = 20 ^ { \circ } , \mathrm { c } _ { 2 } = 1.6$

B) $\mathrm { A } _ { 1 } = 61 ^ { \circ } , \mathrm { C } _ { 1 } = 78 ^ { \circ } , \mathrm { C } _ { 1 } = 0.1$;
$\mathrm { A } _ { 2 } = 119 ^ { \circ } , \mathrm { C } _ { 2 } = 20 ^ { \circ } , \mathrm { C } _ { 2 } = 0.1$
C) $\mathrm { A } = 29 ^ { \circ } , \mathrm { C } = 110 ^ { \circ } , \mathrm { c } = 5.7$
D) no triangle

Question

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
-$\mathrm { B } = 41 ^ { \circ } , \mathrm { a } = 4 , \mathrm {~b} = 3$
A) $\mathrm { A } _ { 1 } = 61 ^ { \circ } , \mathrm { C } _ { 1 } = 78 ^ { \circ } , \mathrm { C } _ { 1 } = 4.5$;
$\mathrm { A } _ { 2 } = 119 ^ { \circ } , \mathrm { C } _ { 2 } = 20 ^ { \circ } , \mathrm { c } _ { 2 } = 1.6$

B) $\mathrm { A } _ { 1 } = 61 ^ { \circ } , \mathrm { C } _ { 1 } = 78 ^ { \circ } , \mathrm { C } _ { 1 } = 0.1$;
$\mathrm { A } _ { 2 } = 119 ^ { \circ } , \mathrm { C } _ { 2 } = 20 ^ { \circ } , \mathrm { C } _ { 2 } = 0.1$
C) $\mathrm { A } = 29 ^ { \circ } , \mathrm { C } = 110 ^ { \circ } , \mathrm { c } = 5.7$
D) no triangle

Quizplus · Accepted Answer

Using the Law of Sines, two possible triangles can be formed: one with angles A1 = 61°, B = 41°, C1 = 78° and another with angles A2 = 119°, B = 41°, C2 = 20°. The side lengths are consistent with these angles.

Use the Law of Sines to Solve, If Possible, the Triangle