Two Sides and an Angle Are Given $\mathrm { a } = 14 , \quad \mathrm {~b} = 12 , \quad \beta = 25 ^ { \circ }$

Multiple Choice

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s) that results.
- $\mathrm { a } = 14 , \quad \mathrm {~b} = 12 , \quad \beta = 25 ^ { \circ }$

A) one triangle
$$\alpha = 150.46 ^ { \circ } , \gamma = 4.54 ^ { \circ } , \mathrm { c } = 2.25$$

B) one triangle
$$\alpha = 29.54 ^ { \circ } , \gamma = 125.46 ^ { \circ } , \mathrm { c } = 23.13$$
C) two triangles
$$\begin{array} { l } \alpha _ { 1 } = 29.54 ^ { \circ } , \gamma _ { 1 } = 125.46 ^ { \circ } , \mathrm { c } _ { 1 } = 23.13 \text { or } \\\alpha _ { 2 } = 150.46 ^ { \circ } , \gamma _ { 2 } = 4.54 ^ { \circ } , \mathrm { c } _ { 2 } = 2.25\end{array}$$
D) no triangle