Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
-$$\mathrm { B } = 20 ^ { \circ } , \mathrm { b } = 11.0 , \mathrm { a } = 16.08$$
A) $\mathrm { A } _ { 1 } = 30 ^ { \circ } , \mathrm { C } _ { 1 } = 130 ^ { \circ } , \mathrm { c } _ { 1 } = 24.6$;
$\mathrm{A}_{2}=150^{\circ}, \mathrm{C}_{2}=10^{\circ}, \mathrm{c}_{2}=5.6$

B) $\mathrm { A } = 30 ^ { \circ } , \mathrm { C } = 130 ^ { \circ } , \mathrm { c } = 24.6$

C) $\mathrm { A } = 150 ^ { \circ } , \mathrm { C } = 10 ^ { \circ } , \mathrm { c } = 5.6$
D) no triangle

Question

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
-$$\mathrm { B } = 20 ^ { \circ } , \mathrm { b } = 11.0 , \mathrm { a } = 16.08$$
A) $\mathrm { A } _ { 1 } = 30 ^ { \circ } , \mathrm { C } _ { 1 } = 130 ^ { \circ } , \mathrm { c } _ { 1 } = 24.6$;
$\mathrm{A}_{2}=150^{\circ}, \mathrm{C}_{2}=10^{\circ}, \mathrm{c}_{2}=5.6$

B) $\mathrm { A } = 30 ^ { \circ } , \mathrm { C } = 130 ^ { \circ } , \mathrm { c } = 24.6$

C) $\mathrm { A } = 150 ^ { \circ } , \mathrm { C } = 10 ^ { \circ } , \mathrm { c } = 5.6$
D) no triangle

Quizplus · Accepted Answer

Given the ambiguous case (SSA), using the Law of Sines, two possible triangles can exist because the given side $a$ is longer than side $b$ and the angle $B$ is acute, leading to two possible angles for $A$ and consequently two different triangles.

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