Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
-$$\mathrm { B } = 112 ^ { \circ } , \mathrm { b } = 4 , \mathrm { a } = 25$$
A) no triangle
B) $\mathrm { A } = 57 ^ { \circ } , \mathrm { C } = 12 ^ { \circ } , \mathrm { c } = 33$
C) $\mathrm { A } = 56 ^ { \circ } , \mathrm { C } = 12 ^ { \circ } , \mathrm { c } = 29$
D) $\mathrm { A } = 55 ^ { \circ } , \mathrm { C } = 12 ^ { \circ } , \mathrm { c } = 31$

Question

Quizplus · Accepted Answer

Given the information, the Law of Sines can be applied as $\frac{a}{\sin A} = \frac{b}{\sin B}$. Plugging in the given values, $\frac{25}{\sin A} = \frac{4}{\sin 112^\circ}$. Solving for $\sin A$ gives a value greater than 1, which is impossible, indicating no such triangle exists.

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