Two Sides and an Angle Are Given $$\mathrm { a } = 7 , \quad \mathrm {~b} = 9 , \quad \beta = 49 ^ { \circ }$$

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.
- $$\mathrm { a } = 7 , \quad \mathrm {~b} = 9 , \quad \beta = 49 ^ { \circ }$$

A) two triangles
$$\begin{array} { l } \alpha _ { 1 } = 76.01 ^ { \circ } , \gamma _ { 1 } = 54.99 ^ { \circ } , \mathrm { c } _ { 1 } = 7.60 \text { or } \\\alpha _ { 2 } = 103.99 ^ { \circ } , \gamma _ { 2 } = 27.01 , \mathrm { c } _ { 2 } = 12.14\end{array}$$

B) one triangle

$$\alpha = 35.94 ^ { \circ } , \gamma = 95.06 ^ { \circ } , \mathrm { c } = 11.88$$

C) one triangle
$$\alpha = 76.01 ^ { \circ } , \gamma = 54.99 ^ { \circ } , \mathrm { c } = 7.60$$

D) no triangle